   Chapter 2.7, Problem 26E

Chapter
Section
Textbook Problem

Sketch the graph of a function f where the domain is (–2, 2), f'(0) = –2, lim x → 2 − f ( x ) = ∞ , f is continuous at all numbers in its domain except ±1, and f is odd.

To determine

To sketch: The graph of a function f(x).

Explanation

Given:

The domain of the function is (2,2).

The derivatives f(0)=2.

The limit limx2f(x)=.

The function is continuous on it’s domain except ±1 and the function is odd.

Calculation:

Here the function is continuous on it’s domain except ±1.

That is, the graph of the function has a cuts at ±1.

The function is odd function ( f(x)=f(x) ). In graphical the graph of the function is symmetric about x-axis and f(0)=f(0).

Thus, f(0)=0.

Note that, the value f(a) means that the instantaneous rate of change of y=f(x) at x when x=a.

The given value f(0)=2

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