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Question Number 29464    Answers: 1   Comments: 0

An arrow is projected straight upwards at a speed of 100m/s. With what speed will it return to the ground if air resistance is ignored?

$${An}\:{arrow}\:{is}\:{projected}\:{straight} \\ $$$${upwards}\:{at}\:{a}\:{speed}\:{of}\:\mathrm{100}{m}/{s}. \\ $$$${With}\:{what}\:{speed}\:{will}\:{it}\:{return}\:{to} \\ $$$${the}\:{ground}\:{if}\:{air}\:{resistance}\:{is} \\ $$$${ignored}? \\ $$

Question Number 29463    Answers: 1   Comments: 0

An object undergoes constant acceleration after starting from rest and then travels 5m in the first second.Determine how far it will go in the next second. a)15m b)10m c)20m d)5m

$${An}\:{object}\:{undergoes}\:{constant} \\ $$$${acceleration}\:{after}\:{starting}\:{from} \\ $$$${rest}\:{and}\:{then}\:{travels}\:\mathrm{5}{m}\:{in}\:{the} \\ $$$${first}\:{second}.{Determine}\:{how}\:{far} \\ $$$${it}\:{will}\:{go}\:{in}\:{the}\:{next}\:{second}. \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left.\mathrm{5}{m}\:\:{b}\right)\mathrm{10}{m}\:{c}\right)\mathrm{20}{m}\:{d}\right)\mathrm{5}{m} \\ $$$$ \\ $$$$ \\ $$

Question Number 29461    Answers: 0   Comments: 1

let give u_n = (1/(√n))( (1/(√1)) +(1/(√2)) +...+(1/(√n))) find lim_(n→+∞) u_(n ) .

$${let}\:{give}\:\:{u}_{{n}} =\:\frac{\mathrm{1}}{\sqrt{{n}}}\left(\:\:\frac{\mathrm{1}}{\sqrt{\mathrm{1}}}\:+\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}\:+...+\frac{\mathrm{1}}{\sqrt{{n}}}\right)\: \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} {u}_{{n}\:} . \\ $$

Question Number 29460    Answers: 2   Comments: 0

find lim_(x→0) ((e^(√(1+sinx)) −e)/(tanx)).

$${find}\:\:\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\frac{{e}^{\sqrt{\mathrm{1}+{sinx}}} \:\:−{e}}{{tanx}}. \\ $$

Question Number 29459    Answers: 0   Comments: 6

find lim_(x→0) (((sinx)/x))^(1/(1−cosx)) .

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\left(\frac{{sinx}}{{x}}\right)^{\frac{\mathrm{1}}{\mathrm{1}−{cosx}}} \:. \\ $$

Question Number 29458    Answers: 0   Comments: 1

fimd lim_(x→0) ((((sinx)/(x(1+x)))−1+x)/x^2 ) .

$${fimd}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\frac{\frac{{sinx}}{{x}\left(\mathrm{1}+{x}\right)}−\mathrm{1}+{x}}{{x}^{\mathrm{2}} }\:. \\ $$

Question Number 29457    Answers: 0   Comments: 0

let give P_n (x)= Π_(k=1) ^n ch((x/2^(k)) )) find lim_(n→+∞) P_n (x) .

$${let}\:{give}\:{P}_{{n}} \left({x}\right)=\:\prod_{{k}=\mathrm{1}} ^{{n}} {ch}\left(\frac{{x}}{\mathrm{2}^{\left.{k}\right)} }\right)\: \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} {P}_{{n}} \left({x}\right)\:. \\ $$

Question Number 29456    Answers: 0   Comments: 1

let give F(x)= ∫_x ^(2x) (dt/(√(1+t^2 +t^4 ))) 1) calculate (dF/dx)(x) 2)find lim_(x→+∞) F(x) and lim_(x→+∞) ((F(x))/x) .

$${let}\:{give}\:{F}\left({x}\right)=\:\int_{{x}} ^{\mathrm{2}{x}} \:\:\:\frac{{dt}}{\sqrt{\mathrm{1}+{t}^{\mathrm{2}} +{t}^{\mathrm{4}} }}\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\frac{{dF}}{{dx}}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{x}\rightarrow+\infty} {F}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow+\infty} \:\frac{{F}\left({x}\right)}{{x}}\:. \\ $$

Question Number 29455    Answers: 1   Comments: 1

find ∫ 3^(√(2x+1)) dx .

$${find}\:\int\:\:\mathrm{3}^{\sqrt{\mathrm{2}{x}+\mathrm{1}}} \:{dx}\:. \\ $$

Question Number 29454    Answers: 0   Comments: 1

f is a function increasing and C^1 on [a,b] prove ∫_(f(a)) ^(f(b)) f^(−1) (t)dt = ∫_a ^b x f^′ (x)dx

$${f}\:{is}\:{a}\:{function}\:{increasing}\:{and}\:{C}^{\mathrm{1}} {on}\:\left[{a},{b}\right]\:{prove} \\ $$$$\:\int_{{f}\left({a}\right)} ^{{f}\left({b}\right)} \:{f}^{−\mathrm{1}} \left({t}\right){dt}\:=\:\int_{{a}} ^{{b}} \:{x}\:{f}^{'} \left({x}\right){dx}\: \\ $$

Question Number 29453    Answers: 0   Comments: 0

study and give the graph of the function f(x)= (x/(1+e^(−(1/x)) )) .

$${study}\:{and}\:{give}\:{the}\:{graph}\:{of}\:{the}\:{function} \\ $$$${f}\left({x}\right)=\:\:\:\:\frac{{x}}{\mathrm{1}+{e}^{−\frac{\mathrm{1}}{{x}}} }\:. \\ $$

Question Number 29452    Answers: 0   Comments: 1

find lim_(n→+∞) Π_(k=1) ^n (1 +(k/n))^(1/n) .

$${find}\:{lim}_{{n}\rightarrow+\infty} \:\:\prod_{{k}=\mathrm{1}} ^{{n}} \:\:\left(\mathrm{1}\:+\frac{{k}}{{n}}\right)^{\frac{\mathrm{1}}{{n}}} \:\:. \\ $$

Question Number 29451    Answers: 0   Comments: 1

find ∫_0 ^(π/4) ln(1+tanx)dx .

$${find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:{ln}\left(\mathrm{1}+{tanx}\right){dx}\:. \\ $$

Question Number 29450    Answers: 0   Comments: 1

find lim_(n→+∞) (1/n^2 )^n (√((n^2 +1^2 )(n^2 +2^2 )....(n^2 +n^(2) ) .))

$${find}\:{lim}_{{n}\rightarrow+\infty} \:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:^{{n}} \sqrt{\left({n}^{\mathrm{2}} +\mathrm{1}^{\mathrm{2}} \right)\left({n}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} \right)....\left({n}^{\mathrm{2}} \:+{n}^{\left.\mathrm{2}\right)\:} .\right.} \\ $$

Question Number 29449    Answers: 0   Comments: 0

find lim_(n→+∞) ^ ^n (√(n!)) .n^(−(n+1)) .

$${find}\:{lim}_{{n}\rightarrow+\infty} ^{} \:^{{n}} \sqrt{{n}!}\:.{n}^{−\left({n}+\mathrm{1}\right)} . \\ $$

Question Number 29448    Answers: 0   Comments: 0

find lim_(x→1) ∫_x ^x^2 ((cos(πt))/(ln(t)))dt .

$${find}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\:\int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\frac{{cos}\left(\pi{t}\right)}{{ln}\left({t}\right)}{dt}\:. \\ $$

Question Number 29447    Answers: 0   Comments: 0

find A_n = ∫_0 ^∞ (dx/((1+x^2 )^n )) with n from N^★ .

$${find}\:\:\:{A}_{{n}} =\:\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} }\:\:{with}\:{n}\:{from}\:{N}^{\bigstar} . \\ $$

Question Number 29446    Answers: 1   Comments: 1

let give a<1 find the value of f(a)= ∫_0 ^(π/2) (dx/(1−acos^2 x)).

$${let}\:{give}\:{a}<\mathrm{1}\:{find}\:{the}\:{value}\:{of} \\ $$$${f}\left({a}\right)=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\mathrm{1}−{acos}^{\mathrm{2}} {x}}. \\ $$

Question Number 29445    Answers: 1   Comments: 0

find ∫ (dx/(sinx +sin(2x))) .

$${find}\:\:\:\int\:\:\:\:\:\:\:\frac{{dx}}{{sinx}\:+{sin}\left(\mathrm{2}{x}\right)}\:. \\ $$

Question Number 29444    Answers: 0   Comments: 1

find ∫_3 ^4 (dx/(x^3 −2x^2 +x−2)) .

$${find}\:\int_{\mathrm{3}} ^{\mathrm{4}} \:\:\:\:\:\:\frac{{dx}}{{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +{x}−\mathrm{2}}\:. \\ $$

Question Number 29443    Answers: 1   Comments: 0

find ∫_0 ^π ((sinx)/(√(1+sin^2 x)))dx

$${find}\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{sinx}}{\sqrt{\mathrm{1}+{sin}^{\mathrm{2}} {x}}}{dx} \\ $$

Question Number 29442    Answers: 1   Comments: 0

splve the d.e xy^′ =(√(x^2 +y^2 )) +y with x>0

$${splve}\:{the}\:{d}.{e}\:\:\:{xy}^{'} =\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:}\:+{y}\:\:{with}\:{x}>\mathrm{0} \\ $$

Question Number 29441    Answers: 0   Comments: 1

find ∫ (x^2 /((2−x^2 )(√(1−x^2 ))))dx

$${find}\:\int\:\:\frac{{x}^{\mathrm{2}} }{\left(\mathrm{2}−{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 29440    Answers: 0   Comments: 0

find ∫_0 ^π ((cosx)/((2+cosx)(3+cosx)))dx

$${find}\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\:\:\frac{{cosx}}{\left(\mathrm{2}+{cosx}\right)\left(\mathrm{3}+{cosx}\right)}{dx} \\ $$

Question Number 29439    Answers: 1   Comments: 0

find ∫_0 ^π (dx/(2+cosx)) .

$${find}\:\int_{\mathrm{0}} ^{\pi} \:\frac{{dx}}{\mathrm{2}+{cosx}}\:. \\ $$

Question Number 29433    Answers: 1   Comments: 0

4(2x^2 )=8^x

$$\mathrm{4}\left(\mathrm{2x}^{\mathrm{2}} \right)=\mathrm{8}^{\mathrm{x}} \\ $$

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