Difference between revisions of "009A Sample Final 3, Problem 1"

Revision as of 19:31, 17 February 2017

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}}

Solution:

(a)

Step 2:

(b)

Step 1:

Step 2:

(c)

@@ Line 1: / Line 1: @@
-<span class="exam">Compute
+<span class="exam">Find each of the following limits if it exists. If you think the limit does not exist provide a reason.
-::<span class="exam">a) <math style="vertical-align: -14px">\lim_{x\rightarrow 4} \frac{\sqrt{x+5}-3}{x-4}</math>
+::<span class="exam">a) <math style="vertical-align: -14px">\lim_{x\rightarrow 0} \frac{\sin(5x)}{1-\sqrt{1-x}}</math>
-::<span class="exam">b) <math style="vertical-align: -14px">\lim_{x\rightarrow 0} \frac{\sin^2x}{3x}</math>
+::<span class="exam">b) <math style="vertical-align: -14px">\lim_{x\rightarrow 8} f(x),</math> given that <math>\lim_{x\rightarrow 8}\frac{xf(x)}{3}=-2</math>
+::<span class="exam">c) <math style="vertical-align: -14px">\lim_{x\rightarrow -\infty} \frac{\sqrt{9x^6-x}}{3x^3+4x}</math>
-::<span class="exam">c) <math style="vertical-align: -14px">\lim_{x\rightarrow -\infty} \frac{\sqrt{x^2+2}}{2x-1}</math>
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