Recent questions tagged limits

The value of $\displaystyle{} \lim_{x \rightarrow 0} \left( \frac{1 – \cos x}{x^{2}}\right)$ is$\frac{1}{4}$$\frac{1}{3}$$\frac{1}{2}$$1$

The value of $\displaystyle{}\lim_{x \to \infty}\left ( \dfrac{1 -e^{-c\left ( 1-x \right )}}{1-x\:e^{-c\left ( 1-x \right )}} \right )$ is$\text{c} \\$$\text{c + 1} \\$$...

$\underset{x \rightarrow 0}{\lim} \bigg( \dfrac{1- \cos x}{x^2} \bigg)$ is$1/4$$1/2$$1$$2$

The value of $\displaystyle{}\lim_{x \rightarrow 0}\dfrac{x^{3}-\sin(x)}{x}$ is$0$$3$$1$$-1$

$\displaystyle{}\lim_{x\rightarrow \infty }\sqrt{x^2+x-1}-x$ is$0$$\infty$$1/2$$-\infty$

$\displaystyle{}\lim_{x\rightarrow 0}\dfrac{\log_e(1+4x)}{e^{3x}-1}$ is equal to$0 \\$$\dfrac{1}{12} \\$$\dfrac{4}{3} \\$$1$

Match the following:$\begin{array}{|l|l|l|l|} \hline P. & \text{Feeler guage} & I. & \text{Radius of an object} \\ \hline Q. & \text{Fillet guage} & II. & \text{Diameter ...

The value of $\displaystyle{\lim_{x\rightarrow 0}\left(\frac{-\sin x}{2\sin x+x\cos x}\right)}$ is ________

In the assembly shown below, the part dimensions are:$L_1 = 22.0^{\pm 0.01} \: mm$,$L_2 = L_3$ = $10.0^{\pm 0.005} \: mm$.Assuming the normal distribution of part dimens...

Holes of diameter $25.0^{{+0.020} \\ {+0.040}}$ $mm$ are assembled interchangeably with the pins of diameter $25.0^{{+0.008}\\{+0.005}}$ $mm$. The minimum clearance in th...

The value of $\displaystyle{} \lim_{x\rightarrow 0}\dfrac{1- \cos(x^2)}{2x^4}$ is$0 \\$$\dfrac{1}{2} \\$$\dfrac{1}{4} \\$undefined

$ \displaystyle{}\lim_{x\rightarrow 0} \left( \dfrac{e^{2x}-1}{\sin(4x)} \right )$ is equal to$0$$0.5$$1$$2$

$\displaystyle{} \lim_{x\rightarrow 0}\dfrac{x- \sin x}{1- \cos x}$ is$0$$1$$3$not defined