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The limit lim h→0 f(x) a = 1 = x^3 (1 + h)³ - 1 h represents f' (a) for some function f and some number a. Find the simplest candidates for f(x) and a. Now notice that in fact any function of the form f(x) = (x + b)³ + c where b and c are real numbers, would yield an acceptable to the question above! In this case at what value of a are we calculating f'(a)? a = 3(1+b)^2 Hint: your answer here may depend on b and/or c. ⠀

The limit lim h→0 f(x) a = 1 = x^3 (1 + h)³ - 1 h represents f' (a) for some function f and some number a. Find the simplest candidates for f(x) and a. Now notice that in fact any function of the form f(x) = (x + b)³ + c where b and c are real numbers, would yield an acceptable to the question above! In this case at what value of a are we calculating f'(a)? a = 3(1+b)^2 Hint: your answer here may depend on b and/or c. ⠀

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The limit lim h→0 f(x)= x^3 1 (1+h)³ - 1 h represents f' (a) for some function f and some number a. Find the simplest candidates for f(x) and a. ⠀ Now notice that in fact any function of the form f(x) = (x + b)³ + c where b and c are real numbers, would yield an acceptable to the question above! In this case at what value of a are we calculating f'(a)? a = 3(1+b)^2 Hint: your answer here may depend on b and/or c.
Transcribed Image Text:The limit lim h→0 f(x)= x^3 1 (1+h)³ - 1 h represents f' (a) for some function f and some number a. Find the simplest candidates for f(x) and a. ⠀ Now notice that in fact any function of the form f(x) = (x + b)³ + c where b and c are real numbers, would yield an acceptable to the question above! In this case at what value of a are we calculating f'(a)? a = 3(1+b)^2 Hint: your answer here may depend on b and/or c.
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