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Chapter 1: Q. 16 (page 153)

Consider the limit expression

limx鈫�42-x4-x

Calculate the limit.

Short Answer

Expert verified

The limit of the expression is鈭�.

Step by step solution

01

Step 1. Given 

The given expression is

limx鈫�42-x4-x

02

Step 2. Calculation

The evaluated expression is

limx鈫�42-x4-x=limx鈫�4(2-x)limx鈫�4(4-x)[Quotientrule]=limx鈫�4(2)-limx鈫�4(x)limx鈫�4(4)-limx鈫�4(x)[DifferenceRule]=2-44-4=2-20=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�3(x+5)=8

limx鈫�0sinxcosx

For each limit statement, use algebra to find 未 or N in terms of 蔚or M, according to the appropriate formal limit definition.

limx鈫�鈭�2+鈥�(1+x+2)=1 find 未 in terms of 蔚.

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

limx鈫�23-4x=-5.

Use the delta-epsilon definition of continuity to argue that f is or is not continuous at the indicated point x=c.

f(x)=2鈭�x,鈥呪赌呪赌呪赌�ifxrationalx2,鈥呪赌呪赌呪赌�ifxirrational,c=1
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