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Resources

Transformations of absolute value functions

Soit l’expression bool\'eenne suivante :

E(x,y,z,t) = xt + x'z't + xy'zt' + x'y't + x'yzt + xy'z'

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l’aide d’un diagramme de Karnaugh, d\'eterminer une somme r\'eduite de cette expression.

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p(x)=5x^{3}-44x^{2}+61x+14

has a known factor of

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(x-7)

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p(x)

as a product of linear factors.

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p(x)=

f

is translated a whole number of units horizontally and vertically to obtain the graph of

h

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f

f(x)=\frac{1}{2} x^{2}

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Write down the expression for

h(x)

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h(x)=

10

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ate the indefinite integral.

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\sin ^{2}(5 x) d x=\square+C

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Integrate by parts with

u=x

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gauss.vaniercollege.qc.ca

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3

ubstitution by parts: blem

10

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ate the indefinite integral.

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x \sin ^{2}(5 x) d x=\square+C .

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Hint: Integrate by parts with

u=x

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20

. Graph the image of triangle RST after it is inht and the

x

-axis then translated

4

units to the ing

3

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What are the vertices of triangle

R^{\prime} S^{\prime} T^{\prime}

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A vonive, dincectly wohday

\Delta s

A=6

B=3

. And the cothue of

B

A=27

177.9700-715 P^{2}+1107

to eash other A larger cincte thas cemre B and passer throught C and D (II) (ii) Finat the area of the shated negren on terms of

,

Use the Ratio Test to determine whether the series is convergent or divergent.

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\sum_{n=1}^{\infty} \frac{14^{n}}{(n+1) 7^{2 n+1}}

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a_{n}

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Evaluate the following limit.

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\lim _{n \rightarrow \infty}\left|\frac{a_{n+1}}{a_{n}}\right|

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\lim _{n \rightarrow \infty}\left|\frac{a_{n+1}}{a_{n}}\right| ? \vee 1,--

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Note: Attempt all questions.

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Usepatital differentiation to evaluate

f_{x}

f_{y}

of the following functions:

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f(x, y, z)=x^{2} \sin x y z

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f(x, y)=3 \ln \left(x^{3}+y^{3}\right)

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2

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Wiserimplicit differentiation to find

\frac{\partial z}{\partial x}

\frac{\partial z}{\partial v}

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3 x^{2} y z^{2}-x \sin y+5 x y=3

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3

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Apply double integral to evaluate the function

f(x, y)=x^{2} y^{2}+x

over the region in the first quadrant bounded by the lines

y=x, y=2 x, x=1, x=2

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4

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Apply line integral to evaluate

\int\left(2 y+x^{2}-z^{2}\right) d

s over the line segment

x=t, y=t^{2}, z=1, \quad 0 \leq t \leq 1

f_{y}

0

f_{y}

1

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5

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\gamma=\left(t, t^{2}, 1\right)

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Solve the homogeneous differential equation

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x^{2} d y-y(x+y) d x=0 \quad, \quad y(0)=1

4

a, b, c, k

be rational numbers such that

k

is not a perfect cube.

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a+b k^{1 / 3}+c k^{2 / 3}

then prove that

a=b=c=0

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a+b k^{i s}+c k^{2 \beta}=0

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Multiplying both sides by

k^{1 / 3}

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a k^{1 / 3}+b k^{2 / 3}+c k=0 \text {. }

Function Evaluation

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Given the function

f(x)=6 x-7

evaluate each of the following.

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A, B

C

, give the exact answer. For

D

E

, give the answer as a simplified expression written in descending order.

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f(0)

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\begin{array}{r} f(0)= \\ f(2)= \\ f(-2)= \\ f(x+1)= \end{array}

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f(x+1)

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f(-x)=

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Enter Game PIN - K...

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Tierra Del Sol Midd.l.

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xamine the triangle at right. Each part is a separate problem. Homework Help

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m \angle D=48^{\circ}

m \angle F=117^{\circ}

m \angle E

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x

m \angle D=4 x+2^{\circ}, m \angle F=7 x-8^{\circ}

m \angle E=4 x+6^{\circ}

. Then calculate

m \angle D

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m \angle D=m \angle F=m \angle E

, what type of triangle is

\triangle F E D

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ive the following systems of equations algebraically and then confirm your solutions by graphing. Homework Help

Dingane has been observing a certain stock for the last few years and he sees that it can be modeled as a function

S(t)

t

(in days) using a sinusoidal expression of the form

a \cdot \sin (b \cdot t)+d

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t=0

, the stock is at its average value of

\$ 3.47

91

25

days later, its value is down to its minimum of

\$ 1.97

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S(t)

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t

should be in radians.

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S(t)=

h(x) = 2^x

change over the interval from

x = 5

x = 6

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h(x)

100\%

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h(x)

2\%

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h(x)

2

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h(x)

2\%

h(x) = 2^x

change over the interval from

x = 1

x = 2

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h(x)

2\%

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h(x)

2

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h(x)

100\%

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h(x)

2\%

g(x)

4

over every unit interval in

x

g(0) = 0

. Which could be a function rule for

g(x)

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g(x) = -4x

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g(x) = 4^x

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g(x) = 4x

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g(x)

-x

4

g

be a function such that

g(4)=8

g^{\prime}(4)=-3

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h

be the function

h(x)=\sqrt{x}

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H

be a function defined as

H(x)=g(x) \cdot h(x)

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H^{\prime}(4)=

1

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Variations et extremums d'une fonction à partir d'une courbe tracée

If the perimeter of a square is

y

, find the area of the square.

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This is a two-step problem. From the list below, choose which step you would do first and which step you would do second to solve the problem:

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4

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4

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E. Take the square root

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F. Take the cube root

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If the perimeter of a square is

y

, find the area of the square.

\bar{a}= \hat{i}+2\hat{j}-\hat{k}

\bar{b}= \hat{i}+\hat{j}-\hat{k}

be two vectors. If

\bar{c}

is a vector such that

\bar{b}\times \bar{c}= \bar{b}\times \bar{a}

\bar{c}\cdot \bar{a}=0

\bar{c}\cdot \bar{b}

9^{x+1}

3^{2x}

as a single term in the form

a(b^{2x})

\int (x'Co_{3}2+2) |4-x| dx

9

. [Maximum Mark:

10

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f(x)=a \log _{2} x

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f^{-1}\left(-\frac{2}{3}\right)=\frac{1}{4}

, find the value of a

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f^{-1}(0)

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f^{-1}(x)=2^{3 x}

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g

is obtained by translating

f^{-1}+1

unit parallel to the

x

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g(x)=\frac{1}{k} \times f^{-1}(x)

\mathrm{k}

is an integer to be evaluated.

2

\int_{0}^{a} f(x) d x=\int_{0}^{a} f(a-x) d x

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\int f(x) d x=g(x)+c

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Consider R.H.S. :

\int_{0}^{a} f(a-x) \mathrm{d} x

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a-x=t

\quad x=a-t

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\therefore \quad-\mathrm{d} x=\mathrm{d} t \Rightarrow \mathrm{d} x=-\mathrm{d} t

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x

0

a, t

varies from a to

0

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I=\int_{a}^{0} f(t)(-\mathrm{d} t)

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=-\int_{a}^{0} f(t) d t

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\int f(x) d x=g(x)+c

0

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\int f(x) d x=g(x)+c

1

as definite integration is

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\int f(x) d x=g(x)+c

2

L.H.S. independent of the variable.

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\int f(x) d x=g(x)+c

3

3

5

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\mathrm{ABCD}

dont le côté mesure

2

\mathrm{F}

, le point milieu du côté

\mathrm{AB}

\mathrm{E}

, un point sur le côté

\mathrm{AD}

tel que la mesure du segment

\mathrm{AE}

\mathrm{X}

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x

, en termes de a, pour que le triangle EFC soit rectangle en

F

20

years younger than Ishaan. Ishaan and Christopher first met two years ago. Fourteen years ago, Ishaan was

3

times as old as Christopher.

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How old is Christopher now?

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Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude

17.0 \times 10^{-22} \mathrm{C} / \mathrm{m}^{2}

\mathbf{E}

: (a) in the outer region of the first plate, (b) in the outer region of the second plate, and (c) between the plates?

p(x)=x^{3}-6 x^{2}+32

has a known factor of

(x-4)

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p(x)

as a product of linear factors.

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p(x)=

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\square

Respon impuls suatu sistem adalah

(\frac{1}{2})^n . U(n)

. Jika sistem tersebut diberi sinyal masukan

2^n . U(n)

. Maka, tentukanlah persamaan sinyal keluaran dari sistem tersebut

Why does multiplying by

10

shift each digit one place to the left?

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(A) Each digit represents

10

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(B) Each digit represents

10

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(C) Each digit represents

10

times its original value.

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(D) Each digit represents

\frac{1}{10}

of its original value.

\frac{d y}{d x}=k y

k

is a constant, and

y(0)=100

y(3)

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100 e^{k}

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\frac{d y}{d x}=k y \rightarrow \int \frac{1}{y} d y+(k d x

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300 e^{k}

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\ln (y)=k x+c

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100 e^{3 k}

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\ln ()=

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300 e^{3 k}

12

. Ala. Ela i Monika maja razem

180

2

razy więcej niz Ala, a Ela

3

razy wieccej niz Monika. Ile pieniędzy ma Monika?

(b) The first snow of the season begins to fall during the night. The depth of the snow,

h

, increases at a constant rate through the night and the following day. At

6

am a snow plough begins to clear the road of snow. The speed,

v \, \text{km/h}

, of the snow plough is inversely proportional to the depth of snow. (This means

v=\frac{A}{h}

A

is a constant.) Let

x \, \text{km}

be the distance the snow plough has cleared and let

t

be the time in hours from the beginning of the snowfall. Let

t=T

6

am. (i) Explain carefully why, for

t \geq T

6

0

6

1

is a constant. (ii) In the period from

6

6

3

am the snow plough clears

6

4

of road, but it takes a further

6

5

hours to clear the next kilometre. At what time did it begin snowing?

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6

Find the distance between a point and a line GWC

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You have prizes to reveal! Go to your game board.

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\ell

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y=-x+3

. Find the distance between

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\ell

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W(5,0)

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Round your answer to the nearest tenth.

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557

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＂ Time ＂],[＂ elapsed ＂]:}

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01

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54

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53

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＂ SmartScore ＂],[＂ out of ＂

100

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Not feeling ready yet? These can help:

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Distance formula (

30

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Graph a linear equation

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Equations of parallel and perpendicular lines (

77

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Lesson: Distance formula

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Lesson: Equations of parallel and perpendicular lines

f(x)=-2x^{2}+7

g(x)=|x-1|

, find all values of

x

, to the nearest tenth, for which

f(x)=g(x)

f(x) = 2x^5 + x^4 - 18x^3 - 17x^2 + 20x + 12

x - 3

f

, what is the value of

f(3)

f(x)=-3 \sec (2 x)

f^{\prime}(x)

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f^{\prime}(x)=

x^{3}+4-5 x^{2}=-5 y+y^{2}

\frac{d y}{d x}

(1,5)

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\left.\frac{d y}{d x}\right|_{(1,5)}=

-5 y+3 y^{2}+4+5 x^{3}=x^{2}

\frac{d y}{d x}

(-1,2)

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\left.\frac{d y}{d x}\right|_{(-1,2)}=

-4-y+x^{2}=y^{2}+3 y^{3}

\frac{d y}{d x}

(-3,1)

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\left.\frac{d y}{d x}\right|_{(-3,1)}=

-5-x^{3}-y^{3}=-3 x^{2}

\frac{d y}{d x}

(2,-1)

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\left.\frac{d y}{d x}\right|_{(2,-1)}=

f(x)

g(x)

are differentiable. The function

h(x)

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h(x) = g(x) - f(x)

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f(2) = 5

f'(2) = -1

g(2) = -7

g'(2) = 3

h'(2)

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Simplify any fractions.

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h'(2) =

f

be a function such that

f(9)=-54

f^{\prime}(9)=6

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h

be the function

h(x)=\sqrt{x}

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\frac{d}{d x}\left[\frac{f(x)}{h(x)}\right]

x=9

g(x)

g(x)

is the translation

1

f(x) = |x|

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Write your answer in the form

a|x - h| + k

a

h

k

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g(x) =

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