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Chapter 1: Q. 40 (page 153)

Indeterminate forms: Identify which of the limit forms listed here are indeterminate. For each form that is not indeterminate, describe the behavior of a limit of that form.

鈭�1.

Short Answer

Expert verified

Given limit form is not indeterminate and it will be always 鈭�.

Step by step solution

01

Step 1. Given Information.

Givenalimitform:鈭�1.

02

Step 2. Indeterminate forms available.

Wehavefollowing7indeterminateformsavailablewithus:鈭�0,鈭�-鈭�,00,鈭�鈭�,00,0脳鈭�,1鈭�.

03

Step 3. Determining the value of the limit form given.

Since, it is clear that it is not an indeterminate form.

Now, it's value will be 鈭�always because whatever be the numerator but if denominator is 1 then it doesn't affect the value in the numerator. If denominator is 1 then it can be ignored and it's value will be equal to numerator as well.

That's why,鈭�1=鈭�.

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Most popular questions from this chapter

Calculate each of the limits:

limh鈫�0(3+h)2-32h.

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

limx鈫�23-4x=-5.

Write each of the inequalities in interval notation:

0<|x+3|<0.05

Write each of the inequalities in interval notation:

fx-L<鈭�

In Exercises 39鈥�44, use Theorem 1.16 and left and right limits to determine whether each function f is continuous at its break point(s). For each discontinuity of f, describe the type of discontinuity and any one-sided discontinuity.

f(x)=-x,ifx<02,ifx=0x,ifx>0.
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