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Chapter 1: Q. 11 (page 148)

Describe in terms of large and small numbers why it makes intuitive sense that limits of the form a1鈭�b0鈭�(c)01must equal 0.

Short Answer

Expert verified

All the three limits equal to zero.

Step by step solution

01

Step 1. Given Information

The given limits are1鈭�,0鈭�,01

02

Step 2. Explanation 

1鈭�is zero because any number divided by infinity approaches to zero.

0鈭�is zero because any number divided by infinity approaches to zero.

01is zero.

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Most popular questions from this chapter

For each limit statement , use algebra to find 未 > 0 in terms of 蔚> 0 so that if 0 < |x 鈭� c| < 未, then | f(x) 鈭� L| < 蔚.

limx鈫�3(x2-2x-3)=0;youmayassume未鈮�1

Each function in Exercises 9鈥�12 is discontinuous at some value x = c. Describe the type of discontinuity and any one-sided continuity at x = c, and sketch a possible graph of f.

limx鈫�2-f(x)=2,limx鈫�2+f(x)=1,f(2)=1.

Write delta-epsilon proofs for each of the limit statements limx鈫�cfx=Lin Exercises 47-60.

limx鈫�03x2+1=1.

Sketch a labeled graph of a function that fails to satisfy the hypothesis of the Intermediate Value Theorem, and illustrate on your graph that the conclusion of the Intermediate Value Theorem does not necessarily hold.

Calculate each of the limits:

limx鈫�1xsin-1x2.
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