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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

Make a rough sketch of the curve y = xn (n an integer) for the following five cases:

(i) n = 0

(ii) n > 0, n odd

(iii) n > 0, n even

(iv) n < 0, n odd

(v) n < 0, n even

Then use these sketches to find The following limits.

(a) lim x 0 + x n

(b) lim x 0 x n

(c) lim x x n

(d) lim x x n

(a)

To determine

To sketch: The curve y=xn for the given five cases and the values of limx0+xn by using sketches.

Explanation

Calculation:

Draw the rough graph of y=xn if n=0, n>0,n is odd, n>0,n is even and n<0,n is odd, n<0,n is even as given below.

From the sketched graph, it is observed:

(i)limx0+xn=1,  y=xn when n=0(ii)limx0+xn=0,  y=xn when n>0,n is odd(iii

(b)

To determine

To find: The values of limx0xn by using the above sketches.

(c)

To determine

To find: The values of limxxn by using the above sketches.

(d)

To determine

To find: The values of limxxn by using the above sketches.

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