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Find
lim_(x rarr oo)(4x^(2)-3x)/(x^(3)).
Choose 1 answer:
(A) 4
(B) 0
(c) -3
(D) The limit is unbounded

Find $\lim _{x \rightarrow \infty} \frac{4 x^{2}-3 x}{x^{3}}$ . $\newline$ Choose $1$ answer: $\newline$ (A) $4$ $\newline$ (B) $0$ $\newline$ (C) $-3$ $\newline$ (D) The limit is unbounded

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Integer inequalities with absolute values

Full solution

Q. Find

\lim _{x \rightarrow \infty} \frac{4 x^{2}-3 x}{x^{3}}

.

\newline

Choose

1

answer:

\newline

(A)

4

\newline

(B)

0

\newline

(C)

-3

\newline

(D) The limit is unbounded

Identify highest power of x: Identify the highest power of x in the denominator. In this case, the highest power of x in the denominator is $x^3$ .
Divide by $x^3$ : Divide every term in the numerator and the denominator by $x^3$ to simplify the expression. This gives us $\frac{4x^2}{x^3}$ - $\frac{3x}{x^3}$ which simplifies to $\frac{4}{x}$ - $\frac{3}{x^3}$ .
Evaluate limits: Evaluate the limit of each term as $x$ approaches infinity. The limit of $\frac{4}{x}$ as $x$ approaches infinity is $0$ because the numerator is constant and the denominator grows without bound. Similarly, the limit of $-\frac{3}{x^3}$ as $x$ approaches infinity is also $0$ for the same reason.
Combine limits: Combine the limits of the individual terms. Since both terms approach $0$ , the limit of the entire expression as $x$ approaches infinity is $0$ .

More problems from Integer inequalities with absolute values

Question

g

can be thought of as a scaled version of

f(x)=|x|

\newline

What is the equation for

g(x)

\newline

1

\newline

g(x)=-\frac{4}{3}|x|

\newline

g(x)=\frac{4}{3}|x|

\newline

g(x)=-\frac{3}{4}|x|

\newline

g(x)=\frac{3}{4}|x|

Posted 2 months ago

Question

y=|x|

is reflected across the

x

-axis and then scaled vertically by a factor of

\frac{5}{3}

\newline

What is the equation of the new graph?

\newline

1

\newline

y=-\frac{5}{3}|x|

\newline

y=\frac{3}{5}|x|

\newline

y=-|x-5|+3

\newline

y=|x-3|+5

Posted 4 months ago

Question

\$ 200

with which to purchase hats and t-shirts that are to be sold at his class' next fundraiser. Each hat costs the same amount of money, and each t-shirt costs the same amount of money. If Aiden spends all his money entirely on hats, he will get

40

hats. If Aiden purchases only

t

-shirts, he will get

80

\mathrm{t}

-shirts. Which of the following best models the relationship between the number of hats,

h

, and the number of

\mathrm{t}

t

, that Aiden could purchase with this money?

\newline

1

\newline

40 h+80 t=400

\newline

80 h+40 t=200

\newline

5 h+2.5 t=200

\newline

2.5 h+5 t=200

Posted 4 months ago

Question

We want to find the intersection points of the graphs given by the following system of equations:

\newline

\left\{\begin{array}{l} x-y=-4 \\ y=5(x+1)^{2}-3 \end{array}\right.

\newline

One of the intersection points is

(-2,2)

\newline

Find the other intersection point. Your answer must be exact.

Posted 4 months ago

Question

\mathbf{2 2}

dollars. Colleen has

x

dollars. Which of the following represents the total amount of money Derrick and Colleen have, in dollars?

\newline

1

\newline

x-22

\newline

x+22

\newline

22 x

\newline

22 x+22

Posted 4 months ago

Question

Wilber wants to make the pond in his backyard bigger. It is currently a cone with a radius of

30

meters and a depth of

15

meters. He wants to increase the radius to

40

meters and the depth to

20

meters. How much more water will the pond hold, in thousands of cubic meters?

\newline

(Round to the nearest thousand cubic meters.)

Posted 1 month ago

Question

Abby is buying a rectangular widescreen TV that she will hang on the wall between two windows such that the longer side of the TV is horizontal. The windows are

36

inches apart horizontally, and a widescreen TV is approximately twice as wide as it is tall. Which of the following could be the diagonal length of a widescreen TV that fits between the windows?

\newline

1

\newline

32

\newline

42

\newline

55

\newline

60

Posted 1 month ago

Question

Ari thinks the perfect milkshake has

5

scoops of ice cream for every

3

spoonfuls of caramel. Freeze Zone makes batches of milkshakes with

10

scoops of ice cream and

7

spoonfuls of caramel.

\newline

What will Ari think about the amount of caramel in Freeze Zone's milkshakes?

\newline

1

\newline

(A) Freeze Zone's milkshakes have too much caramel.

\newline

(B) Freeze Zone's milkshakes have too little caramel.

\newline

(C) Freeze Zone's milkshakes are just right.

Posted 2 months ago

Question

Nayeli lights a

4 \mathrm{~m}^{2}

12

candles. Citlali lights a

10 \mathrm{~m}^{2}

30

of the same type of candles.

\newline

Whose space is lit brighter?

\newline

1

\newline

(A) Nayeli's area

\newline

(B) Citlali's area

\newline

(C) The spaces are equally bright.

Posted 4 months ago

Question

Lashawn makes scrambled eggs with

3

spoonfuls of salsa for every

2

eggs. Gilberta adds

7

spoonfuls of salsa for every

5

\newline

Whose scrambled eggs have a stronger salsa taste?

\newline

1

\newline

(A) Lashawn's eggs

\newline

(B) Gilberta's eggs

\newline

(C) The dishes of scrambled eggs have equal salsa tastes.

Posted 2 months ago