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Old 10-11-2011   #1
qwerty123
 
Join Date: Oct 2011
Posts: 1
Default Calculus Question

1) Evaluate lim ((1/x-1) + (1/(x+1)) / x
x->0

Don't use derivatives for #1

2)Where is the function f(x) = | ln(x)+(sin(e^x)/x^2+5) |
defined, and where is it continuous ?

3) Determine where the function f(x) = (x^2+5x+6)/(x+3) is discontinuous, and define a continuous extension g of f.

4) I KNOW THE ANSWER FOR THIS BUT DON'T KNOW WHAT IT IS ASKING FOR ?

Suppose that x^2-6x-3 <= f(x) <= sqrt(9-x^2) on
[0,3]. Give upper and lower bounds for lim x->0+ f(x) and lim x->3^- f(x)

lim (x^2 - 6x - 3) = -3 as x --> 0+
lim v(9 - x^2) = 3 as x -->0+

-3 = f(x) = 3

lim (x^2 - 6x - 3) = -12 as x --> 3-
lim v(9 - x^2) --> 0 as x --> 3-

-12 = f(x) = 0

(What is the upper bound and lower bound ? I don't know that.)



thanks....please answer these four questions perfectly. Only answer them if ur 100% sure.
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