Chapter 1.1, Problem 34ES

Sketch the graph of the function defined piecewise by the formulaf(x) = {0, x ≤ −1 ; √1 − x^2 , −1 < x < 1 , x, x ≥ 1 ) A positive number _ and the limit L of a function f at a are given. Find a number δ such that|f(x) − L| < _ if 0 < |x − a| < δ.                limx→3  x^2−9/x−3= 6; ϵ = 0.05

Suppose that a function ƒ(x) is defined for all real values of x except x = c. Can anything be said about the existence of lim x approaches c ƒ(x)? Give reasons for your answer.

A. Find lim x->4^+ and lim x->4^- B. Does lim x->4 f(x) exist C. Find lim x->5^+ & lim x->5^- D. Does lim x->5 f(x) exist

If lim f(x)=-2 x-->0+, lim f(x)=3 x-->0-, and f(0)=-2, what can you say about lim f(x) x-->0?

Assuming that lim x→a f(x)/(x−a)2 exists, find lim x→a f(x)/x-a

What is a limit, and what does it mean to say: lim      f(x)=1?                                                                          x->7-

Prove using formal definition. (a) lim x→0+ 1/x = ∞.

a) lim x-->negative a   (f(x)) b) lim x-->postive a   (f(x)) c) lim x-->a.   (f(x))

Consider the function below. f(x) = (1 - 3/x)^x   (a) Use a graph to estimate the value of the limit of  lim x→∞ f(x). correct to two decimal places.   (b) Use a table of values of f(x) to estimate the limit to four decimal places.