Question: Exercise 1. Let f(x) = sin(2x). (a) Find L(x) at a = 0. (b) Use L(x) to approximate sin (0.2). (c) Estimate the error in

Exercise 1. Let f(x) = sin(2x). (a) Find L(x) at a

Exercise 1. Let f(x) = sin(2x). (a) Find L(x) at a = 0. (b) Use L(x) to approximate sin (0.2). (c) Estimate the error in the above approximation. Exercise 2. Let p > 0 be a constant. Define f(x) = (1 + x)? where p > 0 is a constant. (a) Show that at a = 0, L(x) = 1 + px. (b) Use L(x) to approximate (1.2) P. (c) Estimate the error in the above approximation

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!

1 Introduction The derivative of a function f at x is defined in terms of a limit, which may be written as f(x+h) f(x) f(x) = lim h0 . h Figure 1: Graph of the function f(x)=xx over [0,2]. Layered on...

Exercise 3. Let f (x) = tan m. tanx (a) Compute 9133(1) :16 (b) Find L(m) at a = 0. E (c) Use L($) to approximate tan 4 ((1) Estimate the error in the above approximation. Exercise 4. Let f (x) = cos...

5. ax = NI- (1- x2 A. tan x + C B. sin x + C O C. sec | x | + C D. none of these dx 6. x (x2 - 1) 2 A. sec | x | + C O B. cot x + C C. tan x + C O D. none of these9. If f ( x ) = sin (2x), then f '(...

Please help 1 . Let g (x ) = V8 + x . a. Find the linear approximation to g at x = 0. (6 pts ) b. Use the linear approximation you found to approximate 1 8. 09 (4 pts ) . Consider h(x) = x + 2x with...

Math Calculus 110 in chapter 3 Derivatives pls answer with numbers showing the work as math work, not by just writing as words to just explain. pls write on paper with Normal clear handwriting Q3 (11...

IX Math 337-001 Due May 4th, 2015 1. Let f ( x) x 3 for x [0,1]. Given n N , let Pn be the partition of [0,1] defined as 1 2 n Pn {0 x0 , x1 , x2 ,..., xn 1}. n n n a) Find U ( f , Pn ) and L( f , Pn...

1. Let f(x) = tan 2 (x). (a) Find the linearization of f at a = /3. (b) Use the result in part (a) to approximate tan 2 (1) to three decimal places. 2. Findthe exact values of the absolute extrema of...

Math\t107-6381\t-\tQuiz\t#4\t-\tSchultz\t-\tDue\tFebruary\t21,\t2016\t-\tpage\t1\tof 3 Follow\tthese\tdirections\tcarefully. This\tquiz\tis\tdue\tby\t11:59\tEastern\ttime\ton\tFebruary\t21,\t2016. o...

MATH260Week 6 Lab Name: Antiderivatives According to the first part of the fundamental theorem of calculus, the antiderivative reverses the derivative. If f(x) is a derivative, F(x) is the...

Please Help The Taylor series for f (ac ) = ac at -3 is Cn ( 2 + 3 ) " . n=0 Find the first few coefficients. CO = C1 = C2 = C3 C4The Maclaurin series of the function x) 2 5:3 tan1 (91:2) 00 can be...

Capable Cleaners deposits all receipts in the bank each evening and makes all payments by check. On March 31 its ledger balance of cash is $983.40. The bank statement balance of cash as of March 31...

The annual demand for an item is 10,000 units. The cost to process an order is $75 and the inventory holding cost is 2.5% of item cost per quarter. Given the following price breaks for purchasing the...

Which of the following would probably be a fixed cost in an automobile insurance company? a. Application forms b. The salary of customer service representatives c. Time spent by adjusters to evaluate...

Dr. Subaiya broke up the company and sold the following division(s) to a much larger competition: a. the conference division b. the consulting and technology division c. the consulting division d....

2. In this chapter, the reader should reflect on the following concepts: Systemic, positive feedback loop, negative feedback loop, negative feed-back loop dominance, positive feedback loop dominance,...

1. To gain insight into communication situations regarding the fact that they should be understood by examining the relationship between the parts and the whole, and to provide an understanding that...

2. Using a communication conflict you have been involved in, or a problem or phenomenon that you are familiar with, provide answers for a)d). a) Find the critical elements that existed (exist) as you...