Limit of $\frac{\sqrt{1-\mathrm{cos}x}}{x}$ using l'Hôpital

Riya Hansen
2022-07-11
Answered

Limit of $\frac{\sqrt{1-\mathrm{cos}x}}{x}$ using l'Hôpital

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asked 2022-07-27

$lim(\sqrt{{x}^{2}+1}-\sqrt{2})/(x-1)$

x approaches 1

x approaches 1

asked 2022-06-26

Get the limit from

$\underset{x\to \mathrm{\infty}}{lim}(x{\int}_{\frac{\pi}{2}}^{\mathrm{arctan}\left(x\right)}\mathrm{sin}\left({t}^{2}\right)dt\phantom{\rule{mediummathspace}{0ex}})$

$\underset{x\to \mathrm{\infty}}{lim}(x{\int}_{\frac{\pi}{2}}^{\mathrm{arctan}\left(x\right)}\mathrm{sin}\left({t}^{2}\right)dt\phantom{\rule{mediummathspace}{0ex}})$

asked 2022-06-25

If limit is zero:

$\underset{x\to 0}{lim}(\frac{\mathrm{sin}2x}{{x}^{3}}+\frac{a}{{x}^{2}}+b)=0$

then find a+b=?

$\underset{x\to 0}{lim}(\frac{\mathrm{sin}2x}{{x}^{3}}+\frac{a}{{x}^{2}}+b)=0$

then find a+b=?

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How to evaluate the limit $\underset{x\to 0}{lim}\frac{1-\mathrm{cos}(4x)}{{\mathrm{sin}}^{2}(7x)}$

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Find the interval on which the curve C is given by r(t) =(5cost-cos5t)i + (5sint-sin5t)j 0≤t≤2π is smooth

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Determine whether f'(0) exists. $f\left(x\right)={x}^{2}\frac{\mathrm{sin}1}{x}$ if x is not equal to 0, 0 if x=0

asked 2022-06-24

Given :

${S}_{n}=\sum _{k=1}^{n}\frac{1}{k}\text{,}{T}_{n}={\int}_{1}^{n+1}\frac{1}{x}dx$

Find a value of n so that ${S}_{n}\ge 10$

${S}_{n}=\sum _{k=1}^{n}\frac{1}{k}\text{,}{T}_{n}={\int}_{1}^{n+1}\frac{1}{x}dx$

Find a value of n so that ${S}_{n}\ge 10$