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)  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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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