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Chapter 1: Q.8 (page 148)

Determine which of the given forms are indeterminate. For each form that is not indeterminate, describe the behavior of a limit of that form.

鈭�路鈭�0路鈭�5路鈭�5路00.0

Short Answer

Expert verified

The indeterminate forms are0路鈭�and5路鈭�

Step by step solution

01

Step 1. Given Information

The given limits are鈭�路鈭�0路鈭�5路鈭�5路00.0

02

Step 2. identifying Indeterminate forms

鈭�路鈭�is Non-Indeterminate Forms for Limits because the result is also infinity.

0路鈭� is -Indeterminate Forms for Limits because Infinity is an undefined number (having no finite value), multiplying Infinity by Zero results in an undefined value.

5路鈭� is -Indeterminate Forms for Limits Infinity is not considered a number, so infinity times three is technically undefined or no answer, because infinity is not necessarily a number.

5路0is Non-Indeterminate Forms for Limits because any number multiplied by zero is zero.

0路0multiplying by zero always gives 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(x+5)=8

Sketch the graph of a function f described in Exercises 27鈥�32, if possible. If it is not possible, explain why not.

f is left continuous at x = 2 but not continuous at x = 2, and f(2) = 3.

Sketch a labeled graph of a function that satisfies the hypothesis of the Extreme Value Theorem, and illustrate on your graph that the conclusion of the Extreme Value Theorem follows.

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

limx鈫�12x+4=6.

limx鈫�+22x-4
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