   Chapter 2.6, Problem 56E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
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 evenThen 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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