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AllQuestion and Answers: Page 994

Question Number 120036 Answers: 1 Comments: 0

Question Number 120035 Answers: 1 Comments: 0

Question Number 120029 Answers: 0 Comments: 2

Montrer que ∀x∈R cos(sinx)>sin(cosx)

$$\mathrm{Montrer}\:\mathrm{que}\:\forall\mathrm{x}\in\mathbb{R} \\ $$$$\mathrm{cos}\left(\mathrm{sinx}\right)>\mathrm{sin}\left(\mathrm{cosx}\right) \\ $$

Question Number 120028 Answers: 2 Comments: 0

Question Number 120025 Answers: 2 Comments: 0

calculate f^′ (x) 1) f(x) =∫_0 ^∞ ((cos(xt))/(t^2 +x^2 ))dt 2)f(x)=∫_0 ^∞ ((sin(xt^2 +(√2)))/(t^2 +x^2 +3))dt

$$\mathrm{calculate}\:\mathrm{f}^{'} \left(\mathrm{x}\right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{f}\left(\mathrm{x}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{cos}\left(\mathrm{xt}\right)}{\mathrm{t}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} }\mathrm{dt} \\ $$$$\left.\mathrm{2}\right)\mathrm{f}\left(\mathrm{x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{sin}\left(\mathrm{xt}^{\mathrm{2}} +\sqrt{\mathrm{2}}\right)}{\mathrm{t}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} \:+\mathrm{3}}\mathrm{dt} \\ $$

Question Number 120016 Answers: 2 Comments: 0

Question Number 120008 Answers: 2 Comments: 2

Question Number 120006 Answers: 0 Comments: 0

Question Number 119997 Answers: 4 Comments: 0

solve for x,a∈R. (√(x^2 +ax+a^2 ))+(√(x^2 −ax+a^2 ))=1

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{x},\mathrm{a}\in\boldsymbol{\mathrm{R}}. \\ $$$$\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{ax}}+\boldsymbol{{a}}^{\mathrm{2}} }+\sqrt{\boldsymbol{{x}}^{\mathrm{2}} −\boldsymbol{{ax}}+\boldsymbol{{a}}^{\mathrm{2}} }=\mathrm{1} \\ $$

Question Number 119996 Answers: 1 Comments: 0

{ ((x^3 +y^2 =a)),((x^2 +y^3 =b)) :} [solve for:x,y,a≠b∈R]

$$\begin{cases}{\boldsymbol{{x}}^{\mathrm{3}} +\boldsymbol{{y}}^{\mathrm{2}} =\boldsymbol{{a}}}\\{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{3}} =\boldsymbol{{b}}}\end{cases}\:\:\:\left[\boldsymbol{{solve}}\:\boldsymbol{{for}}:\mathrm{x},\mathrm{y},\mathrm{a}\neq\mathrm{b}\in\boldsymbol{\mathrm{R}}\right] \\ $$

Question Number 119989 Answers: 2 Comments: 0

Question Number 119979 Answers: 3 Comments: 1

Question Number 119977 Answers: 2 Comments: 0

lim_(x→∞) ((x^4 )^(1/5) (((x+1))^(1/5) −(x)^(1/5) ))=?

$$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\sqrt[{\mathrm{5}}]{{x}^{\mathrm{4}} }\left(\sqrt[{\mathrm{5}}]{{x}+\mathrm{1}}−\sqrt[{\mathrm{5}}]{{x}}\:\right)\right)=? \\ $$

Question Number 119970 Answers: 3 Comments: 0

∫ (dx/(x^2 (√(25−x^2 )))) ?

$$\:\int\:\frac{{dx}}{{x}^{\mathrm{2}} \sqrt{\mathrm{25}−{x}^{\mathrm{2}} }}\:? \\ $$

Question Number 119969 Answers: 1 Comments: 0

Question Number 119965 Answers: 1 Comments: 0

Question Number 119961 Answers: 3 Comments: 0

Without L′Hopital rule lim_(x→π/3) ((sin (x−(π/3)))/(1−2cos x)) ?

$${Without}\:{L}'{Hopital}\:{rule}\: \\ $$$$\:\underset{{x}\rightarrow\pi/\mathrm{3}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left({x}−\frac{\pi}{\mathrm{3}}\right)}{\mathrm{1}−\mathrm{2cos}\:{x}}\:? \\ $$

Question Number 119960 Answers: 1 Comments: 0

Question Number 119956 Answers: 2 Comments: 0

Given a = 1+3+3^2 +3^3 +3^4 +...+3^(100) Find the remainder of dividing the number by 5 . (a) 2 (b) 0 (c)4 (d)1 (e) 3

$${Given}\:{a}\:=\:\mathrm{1}+\mathrm{3}+\mathrm{3}^{\mathrm{2}} +\mathrm{3}^{\mathrm{3}} +\mathrm{3}^{\mathrm{4}} +...+\mathrm{3}^{\mathrm{100}} \\ $$$${Find}\:{the}\:{remainder}\:{of}\:{dividing}\:{the}\:{number} \\ $$$${by}\:\mathrm{5}\:. \\ $$$$\left({a}\right)\:\mathrm{2}\:\:\:\:\:\left({b}\right)\:\mathrm{0}\:\:\:\:\:\:\:\left({c}\right)\mathrm{4}\:\:\:\:\:\:\left({d}\right)\mathrm{1}\:\:\:\:\:\:\left({e}\right)\:\mathrm{3} \\ $$

Question Number 119939 Answers: 3 Comments: 0

Question Number 119937 Answers: 3 Comments: 0

(i)((1/2)−cos (π/7))((1/2)−cos ((3π)/7))((1/2)−cos ((9π)/7))? (ii) ((√3)+tan 1°)((√3)+tan 2°)((√3)+tan 3°)×...×((√3)+tan 29°)?

$$\:\left({i}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{cos}\:\frac{\pi}{\mathrm{7}}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{cos}\:\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\left(\frac{\mathrm{1}}{\mathrm{2}}−\mathrm{cos}\:\frac{\mathrm{9}\pi}{\mathrm{7}}\right)? \\ $$$$\left({ii}\right)\:\left(\sqrt{\mathrm{3}}+\mathrm{tan}\:\mathrm{1}°\right)\left(\sqrt{\mathrm{3}}+\mathrm{tan}\:\mathrm{2}°\right)\left(\sqrt{\mathrm{3}}+\mathrm{tan}\:\mathrm{3}°\right)×...×\left(\sqrt{\mathrm{3}}+\mathrm{tan}\:\mathrm{29}°\right)? \\ $$

Question Number 119934 Answers: 2 Comments: 0

∫ ((sin^8 x−cos^8 x)/(1−(1/2)sin^2 2x)) dx

$$\:\:\:\int\:\frac{\mathrm{sin}\:^{\mathrm{8}} {x}−\mathrm{cos}\:^{\mathrm{8}} {x}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}{x}}\:{dx}\: \\ $$

Question Number 119933 Answers: 4 Comments: 0

(dx/dy) −y = xy^2

$$\:\frac{{dx}}{{dy}}\:−{y}\:=\:{xy}^{\mathrm{2}} \\ $$

Question Number 119930 Answers: 1 Comments: 0

Question Number 119928 Answers: 2 Comments: 0

Question Number 119922 Answers: 0 Comments: 0

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