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Chapter 1: Q. 57 (page 136)

limx鈫�0sinxcosx

Short Answer

Expert verified

limx鈫�0sinxcosx=0

Step by step solution

01

Step 1. Given information

limx鈫�0sinxcosx

02

Step 2. Plug in the values

limx鈫�0sinxcosx=sin(0)cos(0)

limx鈫�0sinxcosx=0

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Most popular questions from this chapter

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 if x鈭�(c-未,c)鈭�(c,c+未)thenf(x)鈭�(L-蔚,L+蔚).

role="math" localid="1648027918805" limx鈫�2x3=8,蔚=0.5

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�x-1x=1, findNin terms of蔚.

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<0-(x-3),ifx猢�0.

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.

Use what you know about one-sided limits to prove that a function f is continuous at a point x=cif and only if it is both left and right continuous at x=c.
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