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

Revision as of 14:51, 6 March 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)

Step 2:

(b)

Step 1:

Step 2:

(c)

@@ Line 1: / Line 1: @@
 <span class="exam">Compute
-<span class="exam">(a) <math>\lim_{x\rightarrow \infty} \frac{x^{-1}+x}{1+\sqrt{1+x}}</math>
+<span class="exam">(a) &nbsp;<math style="vertical-align: -18px">\lim_{x\rightarrow \infty} \frac{x^{-1}+x}{1+\sqrt{1+x}}</math>
-<span class="exam">(b) <math>\lim_{x\rightarrow 0} \frac{\sin x}{\cos x-1}</math>
+<span class="exam">(b) &nbsp;<math style="vertical-align: -15px">\lim_{x\rightarrow 0} \frac{\sin x}{\cos x-1}</math>
-<span class="exam">(c) <math>\lim_{x\rightarrow 1} \frac{x^3-1}{x^{10}-1}</math>
+<span class="exam">(c) &nbsp;<math style="vertical-align: -15px">\lim_{x\rightarrow 1} \frac{x^3-1}{x^{10}-1}</math>
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"