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LimitsQuestion and Answers: Page 1

Question Number 209926 Answers: 1 Comments: 3

lim_(n→∞) (1/(3n+1))+(1/(3n+2))+...+(1/(4n))

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{3}{n}+\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{3}{n}+\mathrm{2}}+...+\frac{\mathrm{1}}{\mathrm{4}{n}} \\ $$

Question Number 209810 Answers: 1 Comments: 0

lim_( x→0) (( (1+ x )^(1/x) −e)/x) = ?

$$ \\ $$$$\:\:\:\mathrm{lim}_{\:\mathrm{x}\rightarrow\mathrm{0}} \:\frac{\:\left(\mathrm{1}+\:\mathrm{x}\:\right)^{\frac{\mathrm{1}}{\mathrm{x}}} −\mathrm{e}}{\mathrm{x}}\:=\:? \\ $$$$ \\ $$

Question Number 209434 Answers: 0 Comments: 5

Help

$${Help} \\ $$

Question Number 209356 Answers: 1 Comments: 0

Evaluate : lim_( n→∞) Π_(k=0) ^(n−1) cos (((2^( k) .π)/(2^( n) −1)) ) = ?

$$ \\ $$$$\:\:\:\:\:{Evaluate}\:: \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\mathrm{lim}_{\:{n}\rightarrow\infty} \:\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\prod}}\:{cos}\:\left(\frac{\mathrm{2}^{\:{k}} .\pi}{\mathrm{2}^{\:{n}} \:−\mathrm{1}}\:\right)\:\:=\:?\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 209220 Answers: 1 Comments: 0

Question Number 209116 Answers: 1 Comments: 0

Question Number 208816 Answers: 0 Comments: 1

Question Number 208482 Answers: 0 Comments: 0

Question Number 208093 Answers: 1 Comments: 0

lim_(n→∞) (1/n)((a+(1/n))^2 +(a+(2/n))^2 +...+(a+((n−1)/n))^2 )

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{{n}}\left(\left({a}+\frac{\mathrm{1}}{{n}}\right)^{\mathrm{2}} +\left({a}+\frac{\mathrm{2}}{{n}}\right)^{\mathrm{2}} +...+\left({a}+\frac{{n}−\mathrm{1}}{{n}}\right)^{\mathrm{2}} \right) \\ $$

Question Number 207816 Answers: 1 Comments: 1

lim_(x→2) ((((x^2 +4))^(1/3) −(√(x^3 −4)))/( (√(x^2 −4))−((x−2))^(1/3) ))

$$\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{2}} +\mathrm{4}}−\sqrt{\mathrm{x}^{\mathrm{3}} −\mathrm{4}}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{4}}−\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{2}}} \\ $$

Question Number 207528 Answers: 2 Comments: 0

Question Number 207339 Answers: 2 Comments: 0

lim_(x→∞) (((x+a)^(1/x) −x^(1/x) )/((x+b)^(1/x) −x^(1/x) )) =?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left({x}+{a}\right)^{\mathrm{1}/{x}} −{x}^{\mathrm{1}/{x}} }{\left({x}+{b}\right)^{\mathrm{1}/{x}} −{x}^{\mathrm{1}/{x}} }\:=? \\ $$

Question Number 206992 Answers: 1 Comments: 0

$$ \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 206934 Answers: 0 Comments: 3

Question Number 206730 Answers: 1 Comments: 1

find lim_(n→+∞) ∫_0 ^n e^(nx) arctan((x/n))dx

$${find}\:{lim}_{{n}\rightarrow+\infty} \int_{\mathrm{0}} ^{{n}} {e}^{{nx}} \:{arctan}\left(\frac{{x}}{{n}}\right){dx} \\ $$

Question Number 206702 Answers: 2 Comments: 0

lim_(n→∞) (√(cosn+sinn−3^n +4^n ))

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{cos}{n}+\mathrm{sin}{n}−\mathrm{3}^{{n}} +\mathrm{4}^{{n}} } \\ $$

Question Number 206433 Answers: 2 Comments: 0

let f:[0,∞)→R be a continuous function if lim_(n→∞ ) ∫_0 ^1 f(x+n)dx = 2 then lim_(n→∞) f(nx) = ?

$$\:\:\:\:\:\mathrm{let}\:\mathrm{f}:\left[\mathrm{0},\infty\right)\rightarrow\mathbb{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{continuous}\:\mathrm{function}\:\mathrm{if} \\ $$$$\:\:\:\:\underset{\mathrm{n}\rightarrow\infty\:} {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{f}\left(\mathrm{x}+\mathrm{n}\right)\mathrm{dx}\:=\:\mathrm{2} \\ $$$$\:\mathrm{then}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{nx}\right)\:=\:? \\ $$$$\: \\ $$

Question Number 206095 Answers: 2 Comments: 0

Question Number 206069 Answers: 1 Comments: 0

lim_(x→0) ((−x^3 +x)/(sin x))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{−{x}^{\mathrm{3}} +{x}}{\mathrm{sin}\:{x}} \\ $$

Question Number 205916 Answers: 1 Comments: 0

lim_(x→0^+ ) xln(e^x −1)

$${lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:{xln}\left({e}^{{x}} −\mathrm{1}\right) \\ $$

Question Number 205774 Answers: 2 Comments: 0

−−−−−−− Ω = Σ_(n=0) ^∞ (( (−1)^( n) )/((−1)^( n) −n)) = ? −−−−−−−

$$ \\ $$$$\:\:\:\:\:\:−−−−−−− \\ $$$$\:\:\:\:\:\Omega\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\:\left(−\mathrm{1}\right)^{\:{n}} }{\left(−\mathrm{1}\right)^{\:{n}} \:−{n}}\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:−−−−−−− \\ $$

Question Number 205727 Answers: 1 Comments: 4

calculate lim_(x→0) ((e^x −cosx)/x^2 )

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{e}^{{x}} −{cosx}}{{x}^{\mathrm{2}} } \\ $$

Question Number 205716 Answers: 2 Comments: 0

lim_(n→∞) (((2n+1)(2n+3)...(4n+1))/((2n)(2n+2)...(4n))) = ?

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{2}{n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{3}\right)...\left(\mathrm{4}{n}+\mathrm{1}\right)}{\left(\mathrm{2}{n}\right)\left(\mathrm{2}{n}+\mathrm{2}\right)...\left(\mathrm{4}{n}\right)}\:\:=\:\:? \\ $$

Question Number 205580 Answers: 1 Comments: 2

lim_(n→∞) (((2n+1)(2n+3)...(4n+1))/((2n)(2n+2)...(4n))) = ?

Question Number 205448 Answers: 0 Comments: 0

A=lim_(x→0) ((sinx)/x^3 )=?

$${A}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{sinx}}{{x}^{\mathrm{3}} }=? \\ $$

Question Number 205379 Answers: 2 Comments: 0

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