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Chapter 1: Q 73. (page 149)

Calculate the limit.

limx鈫�0+x2csc3x1-cos2x

Short Answer

Expert verified

Answer is鈭�

Step by step solution

01

Step 1. Given information

Limit function islimx鈫�0+x2csc3x1-cos2x

02

Step 2. Explanation

limx鈫�0+x2csc3x1-cos2x=limx鈫�0+x2sin3x11-1-2sin2x=limx鈫�0+1sin3x3x(3x)12sin2xx2=limx鈫�0+16x=鈭�

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Most popular questions from this chapter

What are punctured intervals, and why do we need to use them when discussing limits?

For each limit statement in Exercises 41-44, use algebra to find 未or Nin terms of 蔚or M, according to the appropriate formal limit definition.

limx鈫�鈭�x2+2=鈭�,findNin terms ofM.

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

Write delta-epsilon proofs for each of the limit statements in Exercises 47鈥�60.

limx鈫�5+x-5=0

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
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