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Find the slope of the line tangent to the graph of
f(x)=log_(3)((3-5x)/(2x-5)) at
x=2.
Enter an exact answer.

Find the slope of the line tangent to the graph of $f(x)=\log _{3}\left(\frac{3-5 x}{2 x-5}\right)$ at $x=2$ . $\newline$ Enter an exact answer.

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Find the slope of a tangent line using limits

Full solution

Q. Find the slope of the line tangent to the graph of

f(x)=\log _{3}\left(\frac{3-5 x}{2 x-5}\right)

at

x=2

.

\newline

Enter an exact answer.

Calculate rolls needed: Step $1$ : Identify total tape needed and tape per roll. $\newline$ Total tape needed = $8,000$ cm, Tape per roll = $2,000$ cm. $\newline$ Calculate the number of rolls by dividing the total tape needed by the tape per roll. $\newline$ $8,000 \div 2,000 = 4$ .
Confirm calculation: Step $2$ : Confirm the calculation. $\newline$ Recheck the division to ensure no calculation errors. $\newline$ $8,000$ divided by $2,000$ still equals $4$ .

More problems from Find the slope of a tangent line using limits

Question

Consider the curve given by the equation

x y^{2}+5 x y=50

. It can be shown that

\frac{d y}{d x}=\frac{-y(y+5)}{x(2 y+5)} \text {. }

\newline

Write the equation of the vertical line that is tangent to the curve.

Posted 1 month ago

Question

The rate of change

\frac{d P}{d t}

of the number of algae in a tank is modeled by the following differential equation:

\newline

\frac{d P}{d t}=\frac{2317}{10614} P\left(1-\frac{P}{662}\right)

\newline

t=0

, the number of algae in the tank is

174

and is increasing at a rate of

28

algae per minute. At what value of

P

P(t)

growing the fastest?

\newline

Posted 2 months ago

Question

The rate of change

\frac{d P}{d t}

of the number of bacteria in a tank is modeled by the following differential equation:

\newline

\frac{d P}{d t}=\frac{2}{9849} P(598-P)

\newline

t=0

, the number of bacteria in the tank is

196

and is increasing at a rate of

16

bacteria per minute. At what value of

P

does the graph of

P(t)

have an inflection point?

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Posted 2 months ago

Question

The rate of change

\frac{d P}{d t}

of the number of people infected by a disease is modeled by the following differential equation:

\newline

\frac{d P}{d t}=\frac{45}{125404} P(800-P)

\newline

t=0

, the number of people infected by the disease is

214

and is increasing at a rate of

45

people per hour. What is the limiting value for the total number of people infected by the disease as time increases?

\newline

Posted 2 months ago

Question

Which of the following is a correct interpretation of the expression

\newline

-4+13

\newline

1

\newline

(A) The number that is

4

-13

on the number line

\newline

(B) The number that is

4

to the right of

-13

on the number line

\newline

(C) The number that is

13

-4

on the number line

\newline

(D) The number that is

13

to the right of

-4

on the number line

Posted 2 months ago

Question

f

f(x)=x^{3}+2 \sin (3 x-3)

. Use a calculator to write the equation of the line tangent to the graph of

f

x=0.5

. You should round all decimals to

3

\newline

Posted 2 months ago

Question

f

f(x)=x^{2}-2 x+3 \cos \left(x^{2}-x\right)

. Use a calculator to write the equation of the line tangent to the graph of

f

x=-2.5

. You should round all decimals to

3

\newline

Posted 2 months ago

Question

f

f(x)=x^{2}+x-2 \sin (2 x)

. Use a calculator to write the equation of the line tangent to the graph of

f

x=3

. You should round all decimals to

3

\newline

Posted 2 months ago

Question

f

f(x)=x^{3}+\cos \left(2 x^{2}+5\right)

. Use a calculator to write the equation of the line tangent to the graph of

f

x=1

. You should round all decimals to

3

\newline

Posted 2 months ago

Question

f

f(x)=x^{3}+3-5 \sin \left(x^{2}\right)

. Use a calculator to write the equation of the line tangent to the graph of

f

x=1

. You should round all decimals to

3

\newline

Posted 2 months ago