Difference between revisions of "009A Sample Final 2, Problem 8"

Revision as of 19:29, 17 February 2017

Compute

a)

\lim _{x\rightarrow \infty }{\frac {x^{-1}+x}{1+{\sqrt {1+x}}}}

b)

\lim _{x\rightarrow 0}{\frac {\sin x}{\cos x-1}}

c)

\lim _{x\rightarrow 1}{\frac {x^{3}-1}{x^{10}-1}}

Solution:

(a)

ExpandStep 2:

(b)

ExpandStep 1:

ExpandStep 2:

(c)

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 <span class="exam">Compute
-::<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>\lim_{x\rightarrow \infty} \frac{x^{-1}+x}{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>\lim_{x\rightarrow 0} \frac{\sin x}{\cos x-1}</math>
-::<span class="exam">c) <math style="vertical-align: -14px">\lim_{x\rightarrow -\infty} \frac{\sqrt{x^2+2}}{2x-1}</math>
+::<span class="exam">c) <math>\lim_{x\rightarrow 1} \frac{x^3-1}{x^{10}-1}</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"