Question: Let f(x) = 2 + ln|x| and g(x) = arctanx a. Find the equation of the tangent line to the graph of f when x=e

Let f(x) = 2 + ln|x| and g(x) = arctanx

a. Find the equation of the tangent line to the graph of f when x=e

b. Find the equation of the tangent line to the graph of g when x=3.

c. What is the slope of the tangent line to the graph ofy=(2+lnx)/arctanx when x=1?

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Q:

Use the quotient rule to find the derivative of 6ez + 8 4x5 - 7x7 Use e^x for e". You do not need to expand out your answer. Be careful with parentheses!\f5 tan c If f@) = then f'(x) = f'(1)4 sin r...

Q:

Find the derivative of the following. Show your complete solution. Simplify the final answer. 1. f t =-3t*+2t-4 3 2. y= X 3. fx =x-+5-3x-2 4. g t =t-- 4 5. fx= x -3x-+4 X 3t-+4t -8 6. 9 t = 7. y=3x-4...

Q:

\f15. y = 4x -6x2+12x 2x2 16. y = t3 - tz + 4 17. y = 7ex 18. y = -3In (x) 19. Find the slope of the graph of f (x) = 2 + 3 cosx at (n, -1). 20. Find an equation of the tangent line to the graph of y...

Q:

A retail store estimates that weekly sales 5 and weekly advertising costs x (both in dollars) are related by s = 40.000 - 20.000 9 ' 09004". The CL. these costs are increasing at a rate of $600 per...

Q:

TL1. Find the equation ofthe Tangent Line to the curve TL2. Find an equation for the line that is tangent to the curvey=x2 2X 4- l at the point x=1 and graph y = 5x3 _ 4x2+7, at x=1 the curve and its...

Q:

1. (60 pts True/False. Indicate whether the statement is true or false. If the statement is false, present an explanation or counterexample. (No explanation necessary for each true statement.) (2...

Q:

Suppose that the function f has a continuous second derivative for all 513, and that f(0) = 2,f'(0) = 3, and f\"(0) = 0. Let g be a function whose derivative is given by g'(a:) = 823' (3 f (at) + 2...

Q:

I need from 1 to 6! All questions You must show all your work to receive full credit. 1. (2 points) Find the equation of tangent line to the curve y = x4 - 5x3 + 2 at the point (2, - 22). 2. (2...

Q:

ECET2e Section 2.5 21/10/2016, 02:27 WebAssign ECET2e Section 2.5 (Homework) Current Score : 0 / 15 Thu Aung MATH-UA 121, section 11, Fall 2016 Instructor: Benjamin Harrop-Griffiths Due : Thursday,...

Q:

Assignment 3: Problem 6 Previous Problem Problem List Next Problem (1 point) Evaluate the following limit. If the answer is positive infinite, type "I"; if negative infinite, type "N"; and if it does...

Q:

A merchant buys an item listed at $96 less 33 1/3% from a distributor. Overhead is 32% of cost and profit is 27.5% of cost. For how much should the item be retailed?

Q:

A Malaysian company imported clothing and accessories from a wholesaler in South Korea and is due to make a payment of KRW15 million in three months' time. Exchange rates quoted by a Malaysian bank:...

Q:

1 0 As discussed in the e - book, an inflation lesson from history is that: a . inflation's effect on retirement plans is relatively benign b . equities always beat inflation c . Inflation affects...

Q:

On January 1, 2013, Hyde Corporation purchased bonds with a face value of $300,000 for $308,373.53. The bonds are due June 30, 2016, carry a 13% stated interest rate, and were purchased to yield 12%....

Q:

Illinois Steel is a specialty steel manufacturer that does business in the United States, Canada, and Brazil. Illinois Steel is organized as follows. The parent, Illinois Steel, is incorporated in...

Q:

Radley Products has adopted an ABC costing system. The following manufacturing activities, indirect manufacturing costs, and cost drivers have been identified: The Job Cost Record for Job #624...

Q:

Iowa imposes a tax on the operation of slot machines. The rate is graduated based on slot machine revenues. Can Iowa charge a higher maximum rate to racetrack owners than it does to riverboat owners...

Q:

If you have $50,000 in an interest-bearing savings account that pays 2 percent annual interest, how much interest will you earn during a 30 day month?

Q:

As the business needs change, so may the requests from employees on what's important to them. How does your organization respond to the input/requests from employees? How are they informed of the...

Q:

The temporal rule: The closer temporal proximity we have to an event or action, the more probable it is that the distortion of information is less than if the event or action happened longer ago.

Q:

The relevance of the information to the interpreter

Q:

The first-hand information rule: If an event is communicated to us by someone who witnessed an event at first-hand, we will have more confidence in the information than if we were told about it by...