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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

For f ( x ) = 2 x 1 ln x find each of the following limits.

(a) lim x f ( x )

(b) lim x 0 + f ( x )

(C) lim x 1 f ( x )

(d) lim x 1 + f ( x )

(e) Use the information from parts (a) – (d) to make a rough sketch of the graph of f

(a)

To determine

To find: The value of limxf(x), where f(x)=2x1lnx.

Explanation

Result used:

Limit Laws:

Suppose that c is a constant and the limits limxaf(x) and limxag(x) exists, then

Limit law 1: limxa[f(x)+g(x)]=limxaf(x)+limxag(x)

Limit law 2:limxa[f(x)g(x)]=limxaf(x)limxag(x)

Limit law 3:limxa[cf(x)]=climxaf(x)

Limit law 4:limxa[f(x)g(x)]=limxaf(x)limxag(x)

Limit law 5:limxaf(x)g(x)=limxaf(x)limxag(x) if limxag(x)0

Calculation:

Consider the function f(x)=2x1lnx

(b)

To determine

To find: The value of limx0+f(x) when f(x)=2x1lnx.

(c)

To determine

To find: The value of limx1(2x1lnx).

(d)

To determine

To find: The value of limx1(2x1lnx).

(e)

To determine

To sketch: The graph of f using the results obtained from (a) to (d).

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