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AllQuestion and Answers: Page 1732

Question Number 34571 Answers: 0 Comments: 0

A machine with a velocity ratio of 5 requires 150J of work to raise a 500N load through a vertical distance of 200cm,calculate: a)the efficiency b)the M.A of the machine

$${A}\:{machine}\:{with}\:{a}\:{velocity}\:{ratio} \\ $$$${of}\:\mathrm{5}\:{requires}\:\mathrm{150}{J}\:{of}\:{work}\:{to}\:{raise} \\ $$$${a}\:\mathrm{500}{N}\:{load}\:{through}\:{a}\:{vertical} \\ $$$${distance}\:{of}\:\mathrm{200}{cm},{calculate}: \\ $$$$\left.{a}\right){the}\:{efficiency} \\ $$$$\left.{b}\right){the}\:{M}.{A}\:{of}\:{the}\:{machine} \\ $$

Question Number 34567 Answers: 1 Comments: 0

x determinant ((2),())−2x−15=0

$${x}\begin{vmatrix}{\mathrm{2}}\\{}\end{vmatrix}−\mathrm{2}{x}−\mathrm{15}=\mathrm{0} \\ $$

Question Number 34562 Answers: 1 Comments: 1

find the value of ∫_0 ^1 ((arctanx)/((1+x^2 )^2 )) dx

$${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctanx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx} \\ $$

Question Number 34561 Answers: 0 Comments: 1

find the value of ∫_0 ^(+∞) ((arctan(x))/((1+x^2 )^2 )) dx

$${find}\:{the}\:{value}\:\:{of}\:\:\int_{\mathrm{0}} ^{+\infty} \:\:\frac{{arctan}\left({x}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dx} \\ $$

Question Number 34614 Answers: 0 Comments: 1

decompose inside R(x) the fraction F(x)= (1/((x−3)^6 (x+2))) .

$${decompose}\:{inside}\:{R}\left({x}\right)\:{the}\:{fraction} \\ $$$${F}\left({x}\right)=\:\frac{\mathrm{1}}{\left({x}−\mathrm{3}\right)^{\mathrm{6}} \left({x}+\mathrm{2}\right)}\:. \\ $$

Question Number 34554 Answers: 1 Comments: 3

lim_(x→∞) (((a−1+b^(1/x) )/a))^x = ? (a,b>0)

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{{a}−\mathrm{1}+{b}^{\frac{\mathrm{1}}{{x}}} }{{a}}\right)^{{x}} =\:? \\ $$$$\left({a},{b}>\mathrm{0}\right) \\ $$

Question Number 34546 Answers: 0 Comments: 0

∫(dx/(sinx+cosx+tanx+cosecx+secx+cotx))

$$\int\frac{{dx}}{{sinx}+{cosx}+{tanx}+{cosecx}+{secx}+{cotx}} \\ $$

Question Number 34543 Answers: 0 Comments: 2

Question Number 34540 Answers: 0 Comments: 2

a) lim_(x→(π/4)) (((cos x+sin x)^3 −2(√2))/(1−sin 2x)) =? b) lim_(x→0) (sin x)^(1/x) = ?

$$\left.{a}\right)\:\:\:\:\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{\left(\mathrm{cos}\:{x}+\mathrm{sin}\:{x}\right)^{\mathrm{3}} −\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{1}−\mathrm{sin}\:\mathrm{2}{x}}\:=? \\ $$$$\left.{b}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{sin}\:{x}\right)^{\frac{\mathrm{1}}{{x}}} \:=\:? \\ $$

Question Number 34533 Answers: 2 Comments: 5

Solve for x : 5 log_4 x + 48 log_x 4 = (x/8)

$$\mathrm{Solve}\:\mathrm{for}\:\:\mathrm{x}\::\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{5}\:\mathrm{log}_{\mathrm{4}} \mathrm{x}\:\:\:+\:\:\:\mathrm{48}\:\mathrm{log}_{\mathrm{x}} \mathrm{4}\:\:\:\:=\:\:\:\:\frac{\mathrm{x}}{\mathrm{8}} \\ $$

Question Number 34528 Answers: 1 Comments: 1

Find radius c in terms of radii a and b.

$${Find}\:{radius}\:{c}\:{in}\:{terms}\:{of}\:{radii} \\ $$$${a}\:{and}\:{b}. \\ $$

Question Number 34522 Answers: 0 Comments: 2

lim_(x→0) log _e {((sin (a+(1/x)))/(sin a))}^x , 0<a<(π/2) .

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{log}\:_{{e}} \left\{\frac{\mathrm{sin}\:\left({a}+\frac{\mathrm{1}}{{x}}\right)}{\mathrm{sin}\:{a}}\right\}^{{x}} ,\:\mathrm{0}<{a}<\frac{\pi}{\mathrm{2}}\:. \\ $$

Question Number 34516 Answers: 2 Comments: 1

lim_(x→0) log _(tan^2 x) (tan^2 2x) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{log}\:_{\mathrm{tan}\:^{\mathrm{2}} {x}} \left(\mathrm{tan}\:^{\mathrm{2}} \mathrm{2}{x}\right)\:=\:? \\ $$

Question Number 34504 Answers: 1 Comments: 1

1−(1/2)+(1/3)−(1/5)+.... find the sum of the series

$$\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{5}}+.... \\ $$$${find}\:{the}\:{sum}\:{of}\:{the}\:{series} \\ $$

Question Number 34501 Answers: 1 Comments: 1

Question Number 34500 Answers: 0 Comments: 1

prove tan^(−1) ((1/2)tan2A)+tan^(−1) (cotA)+tan^(−1) (cot^3 A)=0

$${prove} \\ $$$${t}\mathrm{an}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{2}}{tan}\mathrm{2}{A}\right)+\mathrm{tan}^{−\mathrm{1}} \left({cotA}\right)+\mathrm{tan}^{−\mathrm{1}} \left({cot}^{\mathrm{3}} {A}\right)=\mathrm{0} \\ $$

Question Number 34499 Answers: 1 Comments: 0

solve the equation cosh(lnx)−sinh(ln(x/2))=1(3/4)

$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{equation}} \\ $$$$\boldsymbol{\mathrm{cosh}}\left(\boldsymbol{\mathrm{ln}{x}}\right)−\boldsymbol{\mathrm{sinh}}\left(\boldsymbol{\mathrm{ln}}\frac{\boldsymbol{{x}}}{\mathrm{2}}\right)=\mathrm{1}\frac{\mathrm{3}}{\mathrm{4}} \\ $$

Question Number 34485 Answers: 1 Comments: 0

is there a function such that: ∀x≥0;f(x+T_1 )=f(x) ∀x≤0;f(x−T_2 )=f(x) f is diferentiabre in x=0

$$\mathrm{is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{function}\:\mathrm{such}\:\mathrm{that}: \\ $$$$\forall{x}\geqslant\mathrm{0};{f}\left({x}+{T}_{\mathrm{1}} \right)={f}\left({x}\right) \\ $$$$\forall{x}\leqslant\mathrm{0};{f}\left({x}−{T}_{\mathrm{2}} \right)={f}\left({x}\right) \\ $$$${f}\:\mathrm{is}\:\mathrm{diferentiabre}\:\mathrm{in}\:{x}=\mathrm{0} \\ $$

Question Number 34464 Answers: 1 Comments: 0

Evaluate lim_(x→0^+ ) x^(m ) (log x )^n , m,n ∈ N

$$\boldsymbol{{E}}{valuate}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:{x}^{{m}\:} \left({log}\:{x}\:\right)^{{n}} \:,\:{m},{n}\:\in\:\mathbb{N} \\ $$

Question Number 34458 Answers: 2 Comments: 4

lim_(x→0) ((sin x −sin (sin x))/x^3 ) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}\:−\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right)}{{x}^{\mathrm{3}} }\:=\:? \\ $$

Question Number 34446 Answers: 0 Comments: 1

∫_(−π/2) ^(π/2) sin {log (x+(√(x^2 +1)) )} dx =

$$\:\underset{−\pi/\mathrm{2}} {\overset{\pi/\mathrm{2}} {\int}}\:\mathrm{sin}\:\left\{\mathrm{log}\:\left({x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\:\right)\right\}\:{dx}\:= \\ $$

Question Number 34445 Answers: 0 Comments: 1

A1) Events A and B are such that P(A) = (9/(30)), P(B)= (2/5) and P(A ∪ B) = (4/5) find a) P(A ∩ B) b) P(A∣B) c) P(B^ ) 2) A bag contains 3 black balls and 5 white balls. Two balls selected are random without replacement.Find the probability a) of selecting a black and white ball in order b) that the balls are of different colours c) the second ball is white

$$\left.\:{A}\mathrm{1}\right)\:\mathrm{Events}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:{P}\left({A}\right)\:=\:\frac{\mathrm{9}}{\mathrm{30}},\:{P}\left(\boldsymbol{{B}}\right)=\:\frac{\mathrm{2}}{\mathrm{5}}\:{and}\: \\ $$$${P}\left({A}\:\cup\:{B}\right)\:=\:\frac{\mathrm{4}}{\mathrm{5}} \\ $$$$\left.{find}\:{a}\right)\:{P}\left({A}\:\cap\:{B}\right) \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:{b}\right)\:{P}\left({A}\mid{B}\right) \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:{c}\right)\:{P}\left(\bar {{B}}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{A}\:\mathrm{bag}\:\mathrm{contains}\:\mathrm{3}\:\mathrm{black}\:\mathrm{balls}\:\mathrm{and} \\ $$$$\mathrm{5}\:\mathrm{white}\:\mathrm{balls}.\:\mathrm{Two}\:\mathrm{balls}\:\mathrm{selected}\:\mathrm{are} \\ $$$$\mathrm{random}\:\mathrm{without}\:\mathrm{replacement}.\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{probability} \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:{a}\right)\:{of}\:{selecting}\:{a}\:{black}\:{and}\:{white} \\ $$$${ball}\:{in}\:{order} \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:{b}\right)\:{that}\:{the}\:{balls}\:{are}\:{of}\:{different}\:{colours} \\ $$$$\left.\:\:\:\:\:\:\:\:{c}\right)\:{the}\:{second}\:{ball}\:{is}\:{white}\: \\ $$

Question Number 34439 Answers: 1 Comments: 0

lim_(x→∞) (−1)^(x−1) sin (π(√(x^2 +0.5x+1))), where x∈N.

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(−\mathrm{1}\right)^{{x}−\mathrm{1}} \mathrm{sin}\:\left(\pi\sqrt{{x}^{\mathrm{2}} +\mathrm{0}.\mathrm{5}{x}+\mathrm{1}}\right), \\ $$$${where}\:{x}\in\mathbb{N}. \\ $$

Question Number 34438 Answers: 0 Comments: 0

Question Number 34985 Answers: 1 Comments: 0

Question Number 34433 Answers: 1 Comments: 1

find lim_(n→+∞) (1/n)Σ_(k=1) ^(n−1) (√((n+k)/(n−k)))

$${find}\:{lim}_{{n}\rightarrow+\infty} \frac{\mathrm{1}}{{n}}\sum_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} \:\sqrt{\frac{{n}+{k}}{{n}−{k}}} \\ $$

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