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AllQuestion and Answers: Page 1048

Question Number 106655 Answers: 0 Comments: 1

Question Number 106609 Answers: 1 Comments: 1

Prove that (1−sin^2 θ)sec^2 θ=1

$${Prove}\:{that} \\ $$$$\left(\mathrm{1}−{sin}^{\mathrm{2}} \theta\right){sec}^{\mathrm{2}} \theta=\mathrm{1} \\ $$

Question Number 106604 Answers: 7 Comments: 1

Question Number 106596 Answers: 4 Comments: 0

Question Number 106594 Answers: 0 Comments: 4

Question Number 106591 Answers: 1 Comments: 7

Question Number 106588 Answers: 0 Comments: 0

@bemath@ x (d^2 y/dx^2 ) + 3x−(dy/dx) = e^(3x)

$$\:\:\:\:\:\:\:@\mathrm{bemath}@ \\ $$$$\mathrm{x}\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:+\:\mathrm{3x}−\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\mathrm{e}^{\mathrm{3x}} \: \\ $$

Question Number 106583 Answers: 1 Comments: 0

@bemath@ ∫_0 ^(π/2) ((sin x dx)/(sin x+cos x)) =?

$$\:\:\:\:\:\:\:\:\:\:\:@\mathrm{bemath}@ \\ $$$$\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\mathrm{sin}\:\mathrm{x}\:\mathrm{dx}}{\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}}\:=? \\ $$

Question Number 106579 Answers: 1 Comments: 0

Given cos x+cos y=(3/2)+cos (x+y) where x,y ∈ [0,2π ]. find x & y

$$\mathcal{G}\mathrm{iven}\:\mathrm{cos}\:\mathrm{x}+\mathrm{cos}\:\mathrm{y}=\frac{\mathrm{3}}{\mathrm{2}}+\mathrm{cos}\:\left(\mathrm{x}+\mathrm{y}\right) \\ $$$$\mathrm{where}\:\mathrm{x},\mathrm{y}\:\in\:\left[\mathrm{0},\mathrm{2}\pi\:\right].\:\mathrm{find}\:\mathrm{x}\:\&\:\mathrm{y}\: \\ $$

Question Number 106572 Answers: 2 Comments: 2

Question Number 106570 Answers: 3 Comments: 0

(1)∫_0 ^a ((√(a−x))/((√(a−x))+(√x))) dx =? (a) 0 (b) (a/2) (c) a (d) 2a (e) (5/2)a (2) ∫_0 ^(π/4) ((1−tan x)/(1+tan x)) dx =? (a) 0 (b) ln 2 (c) −ln 2 (d) πln 2 (e)(1/2)ln 2 (3) ((√3)+2)^x > 7−4(√3) , find the solution set

$$\left(\mathrm{1}\right)\underset{\mathrm{0}} {\overset{\mathrm{a}} {\int}}\:\frac{\sqrt{\mathrm{a}−\mathrm{x}}}{\sqrt{\mathrm{a}−\mathrm{x}}+\sqrt{\mathrm{x}}}\:\mathrm{dx}\:=? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{0}\:\:\:\:\:\:\left(\mathrm{b}\right)\:\frac{\mathrm{a}}{\mathrm{2}}\:\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{a}\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{2a}\:\:\:\:\:\:\left(\mathrm{e}\right)\:\frac{\mathrm{5}}{\mathrm{2}}\mathrm{a} \\ $$$$\left(\mathrm{2}\right)\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\frac{\mathrm{1}−\mathrm{tan}\:\mathrm{x}}{\mathrm{1}+\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\:=? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{0}\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{ln}\:\mathrm{2}\:\:\:\:\:\left(\mathrm{c}\right)\:−\mathrm{ln}\:\mathrm{2}\:\:\:\:\:\left(\mathrm{d}\right)\:\pi\mathrm{ln}\:\mathrm{2}\:\:\:\left(\mathrm{e}\right)\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\mathrm{2} \\ $$$$\left(\mathrm{3}\right)\:\left(\sqrt{\mathrm{3}}+\mathrm{2}\right)^{\mathrm{x}} \:>\:\mathrm{7}−\mathrm{4}\sqrt{\mathrm{3}}\:,\:\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{set} \\ $$

Question Number 107247 Answers: 1 Comments: 0

Question Number 106559 Answers: 0 Comments: 1

sen(7)=

$${sen}\left(\mathrm{7}\right)= \\ $$

Question Number 106555 Answers: 2 Comments: 1

∫_0 ^4 ∫_(√y) ^2 (1/(1+x^3 ))dx dy

$$\int_{\mathrm{0}} ^{\mathrm{4}} \int_{\sqrt{{y}}} ^{\mathrm{2}} \frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{3}} }{dx}\:{dy} \\ $$

Question Number 106548 Answers: 3 Comments: 0

lim_(x→C) ((2x+c)/(x−c))

$${lim}_{{x}\rightarrow{C}} \:\frac{\mathrm{2}{x}+{c}}{{x}−{c}} \\ $$

Question Number 106552 Answers: 0 Comments: 0

Question Number 106526 Answers: 0 Comments: 2

Question Number 106515 Answers: 1 Comments: 0

Sum up the following to nth term: (5/3)+((10)/8)+((17)/(15))+((26)/(24))+........

$${Sum}\:{up}\:{the}\:{following}\:{to}\:{nth}\:{term}: \\ $$$$\:\:\:\:\:\:\:\:\:\frac{\mathrm{5}}{\mathrm{3}}+\frac{\mathrm{10}}{\mathrm{8}}+\frac{\mathrm{17}}{\mathrm{15}}+\frac{\mathrm{26}}{\mathrm{24}}+........ \\ $$

Question Number 106508 Answers: 0 Comments: 6

Question Number 106505 Answers: 2 Comments: 0

Show thatlim_(n→∞) [((n!)/((n−x)!n^x ))]=1

$$\mathrm{Show}\:\mathrm{that}\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left[\frac{\mathrm{n}!}{\left(\mathrm{n}−\mathrm{x}\right)!\mathrm{n}^{\mathrm{x}} }\right]=\mathrm{1} \\ $$

Question Number 106503 Answers: 0 Comments: 11

(2/3)+(2/(18))+(2/(27))+(2/(324))+....

$$\frac{\mathrm{2}}{\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{18}}+\frac{\mathrm{2}}{\mathrm{27}}+\frac{\mathrm{2}}{\mathrm{324}}+.... \\ $$

Question Number 106493 Answers: 1 Comments: 1

Solve? (1)cos(70) (2)cos(10)

$${Solve}? \\ $$$$\left(\mathrm{1}\right){cos}\left(\mathrm{70}\right) \\ $$$$\left(\mathrm{2}\right){cos}\left(\mathrm{10}\right) \\ $$

Question Number 106488 Answers: 3 Comments: 1

Question Number 106479 Answers: 3 Comments: 0

Question Number 106469 Answers: 2 Comments: 0

Solve cos^2 x+3cos^2 2x=cos^2 3x

$$\mathrm{Solve}\:\mathrm{cos}^{\mathrm{2}} \mathrm{x}+\mathrm{3cos}^{\mathrm{2}} \mathrm{2x}=\mathrm{cos}^{\mathrm{2}} \mathrm{3x} \\ $$

Question Number 106468 Answers: 1 Comments: 0

4cos x cos 2x cos 3x = 1

$$\mathrm{4cos}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{2x}\:\mathrm{cos}\:\mathrm{3x}\:=\:\mathrm{1} \\ $$

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