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AllQuestion and Answers: Page 1109

Question Number 106118 Answers: 1 Comments: 1

Question Number 106125 Answers: 2 Comments: 0

∫_(π/4) ^π (√(1−sin2x)) dx

$$\int_{\frac{\pi}{\mathrm{4}}} ^{\pi} \sqrt{\mathrm{1}−\mathrm{sin2}{x}}\:\mathrm{d}{x} \\ $$

Question Number 106156 Answers: 2 Comments: 1

Given { (((√(xy)) +(1/(√x)) +(1/(√y)) =9)),(((√x)+(√y) = 20)) :} where x > y. find the value of x(√y) −y(√x) .

$$\mathrm{Given}\:\begin{cases}{\sqrt{\mathrm{xy}}\:+\frac{\mathrm{1}}{\sqrt{\mathrm{x}}}\:+\frac{\mathrm{1}}{\sqrt{\mathrm{y}}}\:=\mathrm{9}}\\{\sqrt{\mathrm{x}}+\sqrt{\mathrm{y}}\:=\:\mathrm{20}}\end{cases} \\ $$$$\mathrm{where}\:\mathrm{x}\:>\:\mathrm{y}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{x}\sqrt{\mathrm{y}}\:−\mathrm{y}\sqrt{\mathrm{x}}\:. \\ $$

Question Number 106120 Answers: 1 Comments: 3

question 106075 again ∫((1+cosx)/((99cosx−70sinx+210)cosx−66sinx+110))dx=? using t=tan(x/2) I get −4∫(dt/(t^4 +8t^3 −22t^2 +272t−419)) can someone factorize the denominator?

$${question}\:\mathrm{106075}\:{again} \\ $$$$\int\frac{\mathrm{1}+{cosx}}{\left(\mathrm{99}{cosx}−\mathrm{70}{sinx}+\mathrm{210}\right){cosx}−\mathrm{66}{sinx}+\mathrm{110}}{dx}=? \\ $$$${using}\:{t}={tan}\left({x}/\mathrm{2}\right)\:{I}\:{get} \\ $$$$−\mathrm{4}\int\frac{{dt}}{{t}^{\mathrm{4}} +\mathrm{8}{t}^{\mathrm{3}} −\mathrm{22}{t}^{\mathrm{2}} +\mathrm{272}{t}−\mathrm{419}} \\ $$$${can}\:{someone}\:{factorize}\:{the}\:{denominator}? \\ $$

Question Number 106098 Answers: 1 Comments: 0

∫_(1/(2014)) ^(2014) ((tan^(−1) x)/x) dx

$$\int_{\frac{\mathrm{1}}{\mathrm{2014}}} ^{\mathrm{2014}} \frac{\mathrm{tan}^{−\mathrm{1}} {x}}{{x}}\:{dx} \\ $$

Question Number 106101 Answers: 1 Comments: 0

Question Number 106094 Answers: 0 Comments: 6

Question Number 106077 Answers: 0 Comments: 0

Given Σ_(n = 0) ^∞ cos^(2n) (θ) = 5. find the value of cos 2θ+cos 4θ+cos 8θ+cos 16θ+cos 32θ+...= (a) (1/5) (b) (3/5) (c) 2 (d) 1 (e) 3

$$\mathcal{G}\mathrm{iven}\:\underset{\mathrm{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\mathrm{cos}\:^{\mathrm{2n}} \left(\theta\right)\:=\:\mathrm{5}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{cos}\:\mathrm{2}\theta+\mathrm{cos}\:\mathrm{4}\theta+\mathrm{cos}\:\mathrm{8}\theta+\mathrm{cos}\:\mathrm{16}\theta+\mathrm{cos} \\ $$$$\mathrm{32}\theta+...= \\ $$$$\left(\mathrm{a}\right)\:\frac{\mathrm{1}}{\mathrm{5}}\:\:\:\:\:\left(\mathrm{b}\right)\:\frac{\mathrm{3}}{\mathrm{5}}\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{2}\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{1}\:\:\:\:\:\:\left(\mathrm{e}\right)\:\mathrm{3} \\ $$

Question Number 106076 Answers: 2 Comments: 0

solve this pls x^x^(1/2) =(1/2)

$${solve}\:{this}\:{pls} \\ $$$${x}^{{x}^{\frac{\mathrm{1}}{\mathrm{2}}} } =\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 106075 Answers: 1 Comments: 0

∫((1+cosx)/((99cosx−70sinx+210)cosx−66sinx+110))dx=?

$$\int\frac{\mathrm{1}+{cosx}}{\left(\mathrm{99}{cosx}−\mathrm{70}{sinx}+\mathrm{210}\right){cosx}−\mathrm{66}{sinx}+\mathrm{110}}{dx}=? \\ $$

Question Number 106072 Answers: 2 Comments: 0

Question Number 106070 Answers: 0 Comments: 0

Question Number 106065 Answers: 0 Comments: 0

x^2 (d^2 y/dx^2 ) −x (dy/dx) +y = x

$$\mathrm{x}^{\mathrm{2}} \:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:−\mathrm{x}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:+\mathrm{y}\:=\:\mathrm{x}\: \\ $$

Question Number 106044 Answers: 1 Comments: 0

Given f(x)=2x+m, f^(2 ) (x)=px+6 Find the value of m and p.

$$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}+\mathrm{m},\:\mathrm{f}^{\mathrm{2}\:} \left(\mathrm{x}\right)=\mathrm{px}+\mathrm{6} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{m}\:\mathrm{and}\:\mathrm{p}. \\ $$

Question Number 106039 Answers: 3 Comments: 0

if (f o g )(x) = x and f′(x)=1 + (f(x))^2 then g′(2) = ....

$${if}\:\:\left({f}\:{o}\:{g}\:\right)\left({x}\right)\:=\:{x}\:\:{and}\:{f}'\left({x}\right)=\mathrm{1}\:+\:\left({f}\left({x}\right)\right)^{\mathrm{2}} \\ $$$${then}\:{g}'\left(\mathrm{2}\right)\:=\:.... \\ $$$$ \\ $$

Question Number 106033 Answers: 16 Comments: 0

Question Number 106032 Answers: 0 Comments: 2

Version 2.127 is added. • automatically scroll hine in horizontal direction (requested by Mr W) • automatically scrolls to new line to bring newly added line in focus.

$$\mathrm{Version}\:\mathrm{2}.\mathrm{127}\:\mathrm{is}\:\mathrm{added}. \\ $$$$\bullet\:\mathrm{automatically}\:\mathrm{scroll}\:\mathrm{hine}\:\mathrm{in}\:\mathrm{horizontal} \\ $$$$\:\:\:\mathrm{direction}\:\left(\mathrm{requested}\:\mathrm{by}\:\mathrm{Mr}\:\mathrm{W}\right) \\ $$$$\bullet\:\mathrm{automatically}\:\mathrm{scrolls}\:\mathrm{to}\:\mathrm{new}\:\mathrm{line}\:\mathrm{to} \\ $$$$\:\:\:\mathrm{bring}\:\mathrm{newly}\:\mathrm{added}\:\mathrm{line}\:\mathrm{in}\:\mathrm{focus}. \\ $$

Question Number 106029 Answers: 1 Comments: 1