Find the limit and discuss the continuity of the function.

BolkowN
2021-06-26
Answered

Find the limit and discuss the continuity of the function.

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Adnaan Franks

Answered 2021-06-27
Author has **92** answers

substituting

function is continuous everywhere

asked 2022-01-29

Evaluating trig limit $\underset{x\to 0}{lim}\frac{\sqrt{1-\mathrm{cos}\left({x}^{2}\right)}}{1-\mathrm{cos}\left(x\right)}$

I have tried to simplify the expression using the identity$1-\mathrm{cos}\left(x\right)=2{\mathrm{sin}}^{2}\left(\frac{x}{2}\right)$ , but I have still failed to remove the indeterminate form.

I have tried to simplify the expression using the identity

asked 2021-03-04

The limit as x approaches zero of
$\frac{\mathrm{sin}x-x\mathrm{cos}x}{{x}^{3}}$

asked 2022-05-15

I want to calculate the limit of

$\underset{x\to 0}{lim}\frac{1-\mathrm{cosh}({x}^{5})}{{x}^{6}{\mathrm{sin}}^{2}({x}^{2})}$

$\underset{x\to 0}{lim}\frac{1-\mathrm{cosh}({x}^{5})}{{x}^{6}{\mathrm{sin}}^{2}({x}^{2})}$

asked 2022-05-22

Use continuity to evaluate the limit.

$\underset{x\to 3}{lim}\mathrm{arctan}\left(\frac{{x}^{2}-9}{5{x}^{2}-15x}\right)$

Factored and got...

$\underset{x\to 3}{lim}\mathrm{arctan}\left(\frac{x+3}{5x}\right)$

$\underset{x\to 3}{lim}\mathrm{arctan}\left(\frac{{x}^{2}-9}{5{x}^{2}-15x}\right)$

Factored and got...

$\underset{x\to 3}{lim}\mathrm{arctan}\left(\frac{x+3}{5x}\right)$

asked 2021-11-11

Find the limit or show that it does not exist.

$\underset{x\to \mathrm{\infty}}{lim}=\frac{1-{x}^{2}}{{x}^{3}-x+1}$

asked 2021-06-08

Use the limit definition of the derivative to calculate the derivatives of the following function:

(a)$f(x)=4{x}^{2}+3x+1$

(b)$f(x)=\frac{2}{{x}^{2}}$

(a)

(b)

asked 2022-05-22

How to prove that ${\int}_{0}^{\mathrm{\infty}}\mathrm{cos}(\alpha t){e}^{-\lambda t}\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}t=\frac{\lambda}{{\alpha}^{2}+{\lambda}^{2}}$ using real methods?