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Chapter 1: Q. 63 (page 149)

Calculate each limit in Exercises 35鈥�80.

limx鈫�3+ln(x2-9)

Short Answer

Expert verified

The limit is-鈭�

Step by step solution

01

Step 1. Given information     

The given expression is limx鈫�3+ln(x2-9)

02

Step 2. Calculation  

The limit is calculated as below,

limx鈫�3+ln(x2-9)=ln(32-9)=ln(9-9)=ln(0)=-鈭�

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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�-2(4-2x)=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.

Write a delta鈥揺psilon proof that proves that fis continuous on its domain. In each case, you will need to assume that 未 is less than or equal to 1.

f(x)=x2

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-3),ifx<3-(x-3),ifx猢�3.

For each limit limx鈫�cf(x)=Lin Exercises 43鈥�54, use graphs and algebra to approximate the largest value of 未such that ifx鈭�(c-未,c)鈭�(c,c+未)thenf(x)鈭�(L-蔚,L+蔚)

limx鈫�-1x2-2x-3x+1=-4,蔚=0.1
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