009A Sample Final 3, Problem 1

Find each of the following limits if it exists. If you think the limit does not exist provide a reason.

(a) $\lim _{x\rightarrow 0}{\frac {\sin(5x)}{1-{\sqrt {1-x}}}}$

(b) $\lim _{x\rightarrow 8}f(x),$ given that $\lim _{x\rightarrow 8}{\frac {xf(x)}{3}}=-2$

(c) $\lim _{x\rightarrow -\infty }{\frac {\sqrt {9x^{6}-x}}{3x^{3}+4x}}$

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

Final Answer:
(a)
(b)
(c)

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