Find the function The following limits represent the slope

Chapter 4, Problem 65AE

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QUESTION:

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.

\(\lim _{x \rightarrow 2}\ \frac{\frac{1}{x+1}-\frac{1}{3}}{x-2}\)

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QUESTION:

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.

\(\lim _{x \rightarrow 2}\ \frac{\frac{1}{x+1}-\frac{1}{3}}{x-2}\)

ANSWER:

SOLUTION STEP 1 Given is the slope of the curve y=f(x) Thus it is the derivative of the function f(x). 1 1 ie,f(x) = lim x+13 x2 x2 Thus comparing with the definition of t

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