Recent questions tagged limits

1 votes
1 answer
1
Evaluate the following limit:\[\lim _{x \rightarrow 0} \frac{\ln \left(\left(x^{2}+1\right) \cos x\right)}{x^{2}}= \]
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4
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5
How do we solve this question: $\lim n \to \infty \sqrt{n^2 + n} - {\sqrt{n^2 +1}}$
1 votes
1 answer
6
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7
Determine the volume of the solid obtained by rotating the portion of the region bounded by $y=\sqrt[3]{x}$ and $y=\frac{x}{4}$ that lies in the first quadrant about the ...
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8
Depramine the area of region bounded by $y=2x^{2}+10$ and $y=4x+16$
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9
Differentiate each of the following. $g(x)=\int ^{x}_{-4}e^{2t}cos^{2}(1-5t)dt$
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10
1.Evaluate the following definite integral $\int^{130}_{130}\frac{x^{3}-x\sin(x)+\cos(x)}{x^{^{2}}+1}dx$
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11
Determine all the number(s) c which satisfy the conclusion of Roles' Theorem for the given function and interval $f(x)=x^{2}-2x-8 $ on $ [-1,3]$
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12
sketch the graph of $h(x)=-(x+4)^{3}$ and identify all the relative extrema and absolute extrema of the function.
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13
Use the Squeeze Theorem to determine the value of $\lim_{x\rightarrow 0} x^{4}\sin (\frac{\pi}{x}).$$x^{4}\sin (\frac{\pi}{x}).$
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14
Given that $7x\leq f\left ( x \right )\leq 3x^{2}+2$ for all determine the value of $\lim x\rightarrow 0 f(x)$
3 votes
1 answer
15
Find the value of $\lim_{x \rightarrow 0 } \dfrac{x \tan2x - 2x\tan x}{(1-\cos 2x)^2} \rule{1 in}{.5 pt}.$
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16
the value of $lim_{x- 0}(1-sinx.cosx)^{cosec2x}$ is:A $e^{2}$B $e^{-2}$C$e^{1/2}$D $e^{-1/2}$