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Question Number 69374    Answers: 0   Comments: 1

let S_n =Σ_(k=1) ^n (((−1)^k )/k) 1) calculate S_n interms of n 2) find lim_(n→+∞) S_n

$${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{S}_{{n}} \:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{S}_{{n}} \\ $$

Question Number 69373    Answers: 0   Comments: 2

x^3 −3x−3

$${x}^{\mathrm{3}} −\mathrm{3}{x}−\mathrm{3} \\ $$

Question Number 69585    Answers: 0   Comments: 0

Question Number 69355    Answers: 1   Comments: 0

Find the maximun and minimum values of the function f(x)=x^2 −8x+7 and sketch its graph

$$ \\ $$$${Find}\:{the}\:{maximun}\:{and}\:{minimum}\: \\ $$$${values}\:{of}\:{the}\:{function}\:{f}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{7} \\ $$$${and}\:{sketch}\:{its}\:{graph}\: \\ $$

Question Number 69347    Answers: 1   Comments: 0

If a well is dug 21m deep and 1.4m in radius, how much earth is dug out from it? If the inner wall of well is plastered at Rupees 20 per m^2 . WHAT WILL BE ITS COST ?

$${If}\:{a}\:{well}\:{is}\:{dug}\:\mathrm{21}{m}\:{deep}\:{and}\:\mathrm{1}.\mathrm{4}{m} \\ $$$${in}\:{radius},\:{how}\:{much}\:{earth}\:{is}\:{dug} \\ $$$${out}\:{from}\:{it}?\:{If}\:{the}\:{inner}\:{wall}\:{of} \\ $$$${well}\:{is}\:{plastered}\:{at}\:\:{Rupees}\:\mathrm{20}\: \\ $$$${per}\:{m}^{\mathrm{2}} .\:{WHAT}\:\:\mathbb{WILL}\:\:{BE}\:\:{ITS} \\ $$$$\mathcal{COST}\:? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 69338    Answers: 1   Comments: 1

Question Number 69412    Answers: 1   Comments: 1

Question Number 69411    Answers: 0   Comments: 1

Question Number 69328    Answers: 0   Comments: 1

∫_( 0) ^(π/2) ((φ(x))/(φ(x)+φ((π/2) −x))) dx =

$$\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\phi\left({x}\right)}{\phi\left({x}\right)+\phi\left(\frac{\pi}{\mathrm{2}}\:−{x}\right)}\:{dx}\:= \\ $$

Question Number 69482    Answers: 1   Comments: 1

lim_(n→∞) ((2+cosn)/(4n+sinn)) = ?

$$\underset{{n}\rightarrow\infty} {{lim}}\frac{\mathrm{2}+{cosn}}{\mathrm{4}{n}+{sinn}}\:=\:? \\ $$

Question Number 74637    Answers: 1   Comments: 1

1)calculate f(x)=∫_0 ^1 t^2 (√(x^2 +t^2 ))dt with x>0 2) calculste g(x)=∫_0 ^1 (t^2 /(√(x^2 +t^2 )))dt

$$\left.\mathrm{1}\right){calculate}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {t}^{\mathrm{2}} \sqrt{{x}^{\mathrm{2}} +{t}^{\mathrm{2}} }{dt}\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:{calculste}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{t}^{\mathrm{2}} }{\sqrt{{x}^{\mathrm{2}} +{t}^{\mathrm{2}} }}{dt} \\ $$

Question Number 69319    Answers: 0   Comments: 4

Show that lim_((x,y)→(0,0)) (3/(x^2 + 2y^2 )) does not exist

$$\mathrm{Show}\:\mathrm{that}\: \\ $$$$\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\:\frac{\mathrm{3}}{{x}^{\mathrm{2}} \:+\:\mathrm{2}{y}^{\mathrm{2}} } \\ $$$$\mathrm{does}\:\mathrm{not}\:\mathrm{exist} \\ $$

Question Number 69385    Answers: 2   Comments: 0

Question Number 69327    Answers: 1   Comments: 0

∫_( 0) ^1 ((2^(2x+1) − 5^(2x−1) )/(10^x )) dx =

$$\:\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\frac{\mathrm{2}^{\mathrm{2}{x}+\mathrm{1}} −\:\mathrm{5}^{\mathrm{2}{x}−\mathrm{1}} }{\mathrm{10}^{{x}} }\:{dx}\:=\: \\ $$

Question Number 69293    Answers: 0   Comments: 3

Question Number 69297    Answers: 1   Comments: 1

Question Number 69296    Answers: 0   Comments: 6

Question Number 69314    Answers: 1   Comments: 1

if 5 x y 40 are in GP .find x and y

$${if}\:\mathrm{5}\:{x}\:{y}\:\mathrm{40}\:{are}\:{in}\:{GP}\:.{find}\:{x}\:{and}\:{y} \\ $$

Question Number 69272    Answers: 1   Comments: 0

Question Number 69268    Answers: 1   Comments: 0

Question Number 69261    Answers: 1   Comments: 0

find ∫_0 ^1 xtanx dx

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{xtanx}\:{dx} \\ $$

Question Number 69257    Answers: 0   Comments: 0

∫_(−2) ^( 4) ∣x∣^(2x^3 ) dx = ?

$$\int_{−\mathrm{2}} ^{\:\:\mathrm{4}} \mid\boldsymbol{{x}}\mid^{\mathrm{2}\boldsymbol{{x}}^{\mathrm{3}} } \boldsymbol{{dx}}\:=\:? \\ $$

Question Number 69255    Answers: 1   Comments: 0

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

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

Question Number 69276    Answers: 0   Comments: 3

f(x)=Σ_(k=1) ^n ∣x+k∣ (1) find the values of x such that f(x) is minumum. (2) fund the roots of f(x)−m=0 as example you can set n=100, m=2500.

$${f}\left({x}\right)=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\mid{x}+{k}\mid \\ $$$$\left(\mathrm{1}\right)\:{find}\:{the}\:{values}\:{of}\:{x}\:{such}\:{that}\:{f}\left({x}\right)\: \\ $$$${is}\:{minumum}. \\ $$$$\left(\mathrm{2}\right)\:{fund}\:{the}\:{roots}\:{of}\:{f}\left({x}\right)−{m}=\mathrm{0} \\ $$$$ \\ $$$${as}\:{example}\:{you}\:{can}\:{set}\:{n}=\mathrm{100},\:{m}=\mathrm{2500}. \\ $$

Question Number 69247    Answers: 0   Comments: 1

show that c∣a ⇔ −c∣a.

$${show}\:{that}\: \\ $$$$\:{c}\mid{a}\:\Leftrightarrow\:−{c}\mid{a}. \\ $$

Question Number 69246    Answers: 0   Comments: 0

Explicit ∫_0 ^∞ ((Si(ax))/(x+b)) dx with Si(u)=∫_0 ^u ((sinx)/x)dx

$$\:\:\:{Explicit}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{Si}\left({ax}\right)}{{x}+{b}}\:{dx}\:\:\:{with}\:\:{Si}\left({u}\right)=\int_{\mathrm{0}} ^{{u}} \:\frac{{sinx}}{{x}}{dx} \\ $$

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