Introduction to Limits

Find the value of the limit $\underset{x\to 0}{\lim }{\sin }^{-1}\left(\sec x\right)$

$\underset{x\to 0}{\lim }\left(1+x{e}^{-\frac{1}{x^2}}\sin \left(\frac{1}{x^4}\right)\right)=$

If $\alpha ,\beta$ are the roots of ${\mathrm{x}}^2-\mathrm{ax}+\mathrm{b}=0,$ then $\underset{x\to \alpha }{\lim }\frac{e^{{\mathrm{x}}^2-\mathrm{ax}+\mathrm{b}}-1}{x-\alpha }$ is

Evaluate $\underset{y\to 2}{\lim }\left[\right(y^2-3\left)\right(y+2\left)\right]$.

$f\left(x\right)=\left\{\begin{array}{cc}x,& x<0\\ 0,& x=0\\ x^2,& x>0\end{array}\right.$ then find $\underset{x\to 0}{\lim }f\left(x\right)$

$\underset{x\to 2}{\lim }\frac{3x-9}{x-2}=$

$\underset{x\to 0}{\lim }{x}^{\frac{3}{2}}\left(x>0\right)=$

$\underset{a\to \beta }{\lim }\left[\frac{{\sin }^2\alpha -{\sin }^2\beta }{{\alpha }^2-{\beta }^2}\right]$ is equal to

_____ gives us the instantaneous rate of change of one variable with respect to another.

$\underset{x\to 0}{\lim }x\sec x$ is

$\frac{d}{dx}\left(\log \left(\sqrt{x-1}+\sqrt{x+1}\right)\right)$:

Find the gradient of the curve $y=x^3$.

$\underset{x\to 4}{\lim }\frac{x-4}{\left|x-4\right|}=$

Evaluate : $\underset{x\to 0}{\lim }{\left(-1\right)}^{\left[x\right]},$ where $[·]$ denotes the greatest integer function.

Evaluate : $\underset{x\to 0}{\lim }\frac{\sqrt{1-\cos 2x}}{\sqrt{2}x}$

The value of $\underset{x⟶0}{\lim }\frac{x\left(3e^{\frac{1}{x}}+4\right)}{2-e^{\frac{1}{x}}}=$ ?

The value of $\underset{x\to \frac{\pi }{2}}{\mathrm{l}\mathrm{i}\mathrm{m}}\frac{\left[\frac{x}{3}\right]}{\mathrm{l}\mathrm{n}\left(1+\cot x\right)}$ is equal to (where, $\left[.\right]$ denotes the greatest integer function)

$\underset{x\to 0}{\lim }\left\{\frac{\sin \left[\cos x\right]}{1+\left[\cos x\right]}\right\}=$

If $\underset{x\to \infty }{\lim }\left(\frac{x^2+1}{x+1}-ax-b\right)=0$, then

$\underset{x\to a^{-}}{\lim }\left(\frac{{\left|x\right|}^3}{a}-{\left[\frac{x}{a}\right]}^3\right), \left(a<0\right)$, where $\left[x\right]$ denotes the greatest integer less than or equal to $x$ is