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List of top Mathematics Questions on limits of trigonometric functions

Let \(cos^{-1}\frac{y}{b}\)=\(log_e (\frac{x}{n})^n\), then Ay2+By1+Cy=0 is possible :  (where y2=\(\frac{d^2y}{dx^2}\), y1=\(\frac{dy}{dx}\))
If \(\lim\limits_{x \rightarrow 0} \frac{\sin(2+x)-\sin(2-x)}{x}\)= A cos B, then the values of A and B respectively are
\(\begin{array}{l}\displaystyle \lim_{ x\to 0}\left(\frac{(x+2\cos x)^3 + 2(x+2\cos x)^2 + 3 \sin(x+2\cos x)}{(x+2)^3+2(x+2)^2+3\sin(x+2)}\right)^{\frac{100}{x}} \end{array}\)
is equal to _________.

\(\lim_{{x \to 0}} \limits\) \(\frac{cos(sin x)  -  cos x }{x^4}\) is equal to :

If f(x) = \(\begin{vmatrix}     cosx & 1 & 0 \\     0 & 2cosx & 3 \\     0 & 1 & 2cosx \\ \end{vmatrix}\) then \(\lim\limits_{x\rightarrow\pi} f(x)=\)
\(\lim\limits_{x\rightarrow0}(\frac{\tan x}{\sqrt{2x+4}-2})\) is equal to
$\displaystyle \lim_{x\to0}\left(\frac{\tan \,x}{\sqrt{2x +4} - 2}\right)$ is equal to
The value of $\displaystyle\lim_{n \to \infty} \frac{1}{n} \left\{ \sec^2 \frac{\pi}{4 n} + \sec^2 \frac{2 \pi }{4n} + ..... \sec^2 \frac{n \pi}{4n} \right\}$ is
$\displaystyle\lim_{x\to0} \sqrt{\frac{x-\sin x}{x+\sin^{2}x}} $ is equal to
The value of $\displaystyle\lim_{x\to\infty}\left(\frac{\pi}{2} - \tan^{-1} x\right)^{1/x} $ is
The value of k for which the equation $(K - 2)x^2 + 8x + K + 4 = 0$ has both roots real, distinct and negative is
$\displaystyle\lim_{x\to0} \frac{\sin x}{x}$ is equal to
The value of $\frac{\log_{3} 5 \times \log_{25} 27 \times \log_{49} 7}{\log_{81} 3}$ is

The value of \(\displaystyle \lim_{x \to0} \frac{\sqrt{\frac{1}{2} \left(1-\cos2x\right)}}{x}\)

If sin 5x+sin 3x+sin x = 0, then the value of x other than zero, lying between π0≤×≤π2 is;
$ \frac{\sqrt2 cosx -1}{cot x-1}$ is equal to
$\displaystyle\lim _{x \rightarrow \frac{\pi}{4}} \frac{8 \sqrt{2}-(\cos x+\sin x)^7}{\sqrt{2}-\sqrt{2} \sin 2 x}$ is equal to
The value of $ \lim_{x \to \infty}\left(\frac{x^2 sin \left(\frac{1}{x}\right)-x} {1-|x|}\right)$ is
The value of $\lim_{x \to0} \frac{sin^2x+cosx-1}{x^2}$ is
The value of $\displaystyle \lim_{x \to 0} \frac{\sqrt{1-cos\,x^{2}}}{1-cos\,x}$ is
The value of $ \displaystyle\lim_{x \to 0} \frac{\cos \, x}{\pi - x}$ is

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