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# Answer: Find the function The following limits represent

ISBN: 9780321570567 2

## Solution for problem 67AE Chapter 3.1

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition

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Problem 67AE

The following limits represent the slope of a curve y = f(x) at the point (a, f(x)). Determine a function f and a number a; then, calculate the limit.

$$\lim _{h \rightarrow 0}\ \frac{(2+h)^4-16}{h}$$

Step-by-Step Solution:
Step 1 of 3

SOLUTION STEP 1 Given is the slope of the curve y=f(x) Thus it is the derivative of the function f(x). (2+h) 16 ie,f(a) = lim h h0 Thus comparing with the definition of the derivative f(a+h)f(a) f(a) = lim h h0 4 4 Thus f(a) = 2 f(x) = x 4 Thus we can find that f(x) = x and a = 2 Thus the given function is the slope of a curve y=f(x) at point (2,f(2)) STEP 2 Now we have to calculate the limit. (2+h) 16 2 +4.2 h+6.2 h +4.2.h +h 16 lim = lim h0 h h0 h 16+32h+24h +8h +h 16 h +8h +24h +32h 3 2 lim h = lim h = lim h + 8h + 24h + 32 = 32 h0 h0 h0 (2+h) 16 Thus lim =32 h0 h

Step 2 of 3

Step 3 of 3

##### ISBN: 9780321570567

The answer to “?The following limits represent the slope of a curve y = f(x) at the point (a, f(x)). Determine a function f and a number a; then, calculate the limit.$$\lim _{h \rightarrow 0}\ \frac{(2+h)^4-16}{h}$$” is broken down into a number of easy to follow steps, and 33 words. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The full step-by-step solution to problem: 67AE from chapter: 3.1 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: function, lim, determine, Find, calculate. This expansive textbook survival guide covers 112 chapters, and 7700 solutions. Since the solution to 67AE from 3.1 chapter was answered, more than 436 students have viewed the full step-by-step answer.

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Answer: Find the function The following limits represent