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Solved: Limits The following limits represent the
Chapter 7, Problem 54RE(choose chapter or problem)
54-55. Limits The following limits represent the derivative of a function f at a point a. Find a possible f and a, and then evaluate the limit.
\(\lim _{h \rightarrow 0} \frac{\sin ^{2}\left(\frac{\pi}{4}+h\right)-\frac{1}{2}}{h}\)
Questions & Answers
QUESTION:
54-55. Limits The following limits represent the derivative of a function f at a point a. Find a possible f and a, and then evaluate the limit.
\(\lim _{h \rightarrow 0} \frac{\sin ^{2}\left(\frac{\pi}{4}+h\right)-\frac{1}{2}}{h}\)
ANSWER:Solution Step 1: tan ( 3x11) Given lim x5 x5 The given limits represent the derivative of a function f at a point a. From the data the function f(x) is tan ( 3x 11) and the point a=5 tan ( 3x11) We have f’(5)=lim x5 x5 f(x)f(x ) By the definition of limit f’(x)= lim 0 xx0 x0