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Question Number 82924 Answers: 1 Comments: 2

lim_(x→0) (((√(tan x))−(√(sin x)))/(x^2 (√x)))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{tan}\:\mathrm{x}}−\sqrt{\mathrm{sin}\:\mathrm{x}}}{\mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{x}}} \\ $$

Question Number 82901 Answers: 1 Comments: 0

Question Number 82897 Answers: 1 Comments: 2

Question Number 82891 Answers: 2 Comments: 0

∫ (1/(√(1−x^4 ))) dx = ?

$$\int\:\frac{\mathrm{1}}{\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }}\:\mathrm{dx}\:=\:? \\ $$

Question Number 82887 Answers: 1 Comments: 1

find without using l′hopital lim_(x→0) ((ln(1+cos(x))−ln(2))/x)

$${find}\:{without}\:{using}\:{l}'{hopital} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{{ln}\left(\mathrm{1}+{cos}\left({x}\right)\right)−{ln}\left(\mathrm{2}\right)}{{x}} \\ $$

Question Number 82886 Answers: 0 Comments: 2

prove (tanx+cot^2 x)^2 =sex^2 x+cosec^2 x

$${prove}\: \\ $$$$\left({tanx}+{cot}^{\mathrm{2}} {x}\right)^{\mathrm{2}} ={sex}^{\mathrm{2}} {x}+{cosec}^{\mathrm{2}} {x} \\ $$

Question Number 82883 Answers: 1 Comments: 0

[(e^(−2(√x)) /(√x))−(y/(√x)) ] .(dx/dy) = 1 , x ≠ 0

$$\left[\frac{\mathrm{e}^{−\mathrm{2}\sqrt{\mathrm{x}}} }{\sqrt{\mathrm{x}}}−\frac{\mathrm{y}}{\sqrt{\mathrm{x}}}\:\right]\:.\frac{\mathrm{dx}}{\mathrm{dy}}\:=\:\mathrm{1}\:,\:\mathrm{x}\:\neq\:\mathrm{0} \\ $$

Question Number 82881 Answers: 1 Comments: 2

(√(√(...(√(6561))))) = 3^8^x (60 times) find x

$$ \\ $$$$\sqrt{\sqrt{...\sqrt{\mathrm{6561}}}}\:=\:\mathrm{3}^{\mathrm{8}^{\mathrm{x}} } \:\left(\mathrm{60}\:\mathrm{times}\right) \\ $$$$\mathrm{find}\:\mathrm{x} \\ $$

Question Number 82879 Answers: 0 Comments: 1

prove that ((cos^2 a+sin^2 b)/(sin acos a + sin bcos b)) = cot (a+b)

$$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\frac{\mathrm{cos}\:^{\mathrm{2}} \mathrm{a}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{b}}{\mathrm{sin}\:\mathrm{acos}\:\mathrm{a}\:+\:\mathrm{sin}\:\mathrm{bcos}\:\mathrm{b}}\:=\:\mathrm{cot}\:\left(\mathrm{a}+\mathrm{b}\right) \\ $$

Question Number 82878 Answers: 1 Comments: 3

Question Number 82920 Answers: 1 Comments: 0

calculate lim_(x→0) ((ln(1+ln(1+x)))/x)

$${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{ln}\left(\mathrm{1}+{ln}\left(\mathrm{1}+{x}\right)\right)}{{x}} \\ $$

Question Number 82919 Answers: 1 Comments: 2

bangun datar

$${bangun}\:{datar} \\ $$

Question Number 82872 Answers: 0 Comments: 1

1)find ∫∫_W ((xdx)/(a^2 +x^2 +y^2 )) with W_a →x^2 +y^2 ≤a^2 and x>0 (a>0) 2)calculate ∫∫_W_1 ((xdx)/(x^2 +y^2 +1))

$$\left.\mathrm{1}\right){find}\:\int\int_{{W}} \:\frac{{xdx}}{{a}^{\mathrm{2}} \:+{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} }\:{with} \\ $$$${W}_{{a}} \rightarrow{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:\leqslant{a}^{\mathrm{2}} \:{and}\:{x}>\mathrm{0}\:\:\:\:\:\left({a}>\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\int\int_{{W}_{\mathrm{1}} } \:\:\:\frac{{xdx}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:+\mathrm{1}} \\ $$

Question Number 82871 Answers: 0 Comments: 1

find ∫∫_([0,1]^2 ) ∣x^2 −y^2 ∣dxdy

$${find}\:\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{2}} } \:\:\:\mid{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \mid{dxdy} \\ $$

Question Number 82873 Answers: 1 Comments: 2

Question Number 82867 Answers: 0 Comments: 3

hello prove that ∫_0 ^(+∞) sin(x^4 )dx=sin((π/8))∫_0 ^(+∞) e^(−x^4 ) dx? verry nice day Good Bless You

$${hello}\:{prove}\:{that}\:\int_{\mathrm{0}} ^{+\infty} {sin}\left({x}^{\mathrm{4}} \right){dx}={sin}\left(\frac{\pi}{\mathrm{8}}\right)\int_{\mathrm{0}} ^{+\infty} {e}^{−{x}^{\mathrm{4}} } {dx}? \\ $$$${verry}\:{nice}\:{day}\:{Good}\:{Bless}\:{You} \\ $$

Question Number 82843 Answers: 1 Comments: 0

show that (((1+(√3) i)^4 (1+i)^8 )/((cos100°−i sin100)^3 ))=−256

$${show}\:{that} \\ $$$$\frac{\left(\mathrm{1}+\sqrt{\mathrm{3}}\:{i}\right)^{\mathrm{4}} \left(\mathrm{1}+{i}\right)^{\mathrm{8}} }{\left({cos}\mathrm{100}°−{i}\:{sin}\mathrm{100}\right)^{\mathrm{3}} }=−\mathrm{256} \\ $$

Question Number 82839 Answers: 0 Comments: 8

if the first and fifth terms of arithmetic peogression are equal and the seventh and fourtenth terms of another arithmetic are equal then show that the first term from the first arithmetic is equal the tenth from the second one and so sorry because my english is not so good

$${if}\:{the}\:{first}\:{and}\:{fifth}\:{terms}\:{of}\:{arithmetic} \\ $$$${peogression}\:{are}\:{equal}\:{and}\:{the}\:{seventh} \\ $$$${and}\:{fourtenth}\:{terms}\:{of}\:{another}\:{arithmetic}\:{are} \\ $$$${equal}\:{then}\:{show}\:{that}\:{the}\:{first}\:{term}\:{from} \\ $$$${the}\:{first}\:{arithmetic}\:{is}\:{equal}\:{the}\:{tenth} \\ $$$${from}\:{the}\:{second}\:{one} \\ $$$${and}\:{so}\:{sorry}\:{because}\:{my}\:{english}\:{is} \\ $$$${not}\:{so}\:{good} \\ $$

Question Number 82877 Answers: 1 Comments: 1

1)find xy∈R 2)find x,y∈Z (x+2yi)^6 =8i

$$\left.\mathrm{1}\right){find}\:{xy}\in{R} \\ $$$$\left.\mathrm{2}\right){find}\:{x},{y}\in{Z} \\ $$$$\left({x}+\mathrm{2}{yi}\right)^{\mathrm{6}} =\mathrm{8}{i} \\ $$

Question Number 82821 Answers: 0 Comments: 1

Log_y x+Log_x y =64 find x and y

$${Log}_{{y}} \:{x}+{Log}_{{x}} \:{y}\:=\mathrm{64} \\ $$$${find}\:{x}\:{and}\:{y} \\ $$

Question Number 82806 Answers: 1 Comments: 1

Question Number 82800 Answers: 4 Comments: 2

lim_(x→0) ((1−(√(1+x^2 )) cos 2x)/x^2 )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:\mathrm{cos}\:\mathrm{2}{x}}{{x}^{\mathrm{2}} } \\ $$

Question Number 82794 Answers: 0 Comments: 0

(d^2 y/dx^2 ) + 5x ((dy/dx))^2 −6y=ln x

$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{5}{x}\:\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} −\mathrm{6}{y}={ln}\:{x} \\ $$

Question Number 82792 Answers: 1 Comments: 1

show that if A⊂R^m and B⊂R^n are compact sets. then A×B={(a,b)∈R^(m+n) :a∈A and b∈B}

$${show}\:{that}\:{if}\:{A}\subset\mathbb{R}^{{m}} \:{and}\:{B}\subset\mathbb{R}^{{n}} \:{are}\: \\ $$$${compact}\:{sets}.\: \\ $$$${then}\:{A}×{B}=\left\{\left({a},{b}\right)\in\mathbb{R}^{{m}+{n}} :{a}\in{A}\:{and}\:{b}\in{B}\right\} \\ $$

Question Number 82782 Answers: 1 Comments: 1

(1). 9(9÷3)−6(8÷3)×2 (2). 2(5/3)+3(2/4)

$$\:\: \\ $$$$\:\:\:\left(\mathrm{1}\right).\:\mathrm{9}\left(\mathrm{9}\boldsymbol{\div}\mathrm{3}\right)−\mathrm{6}\left(\mathrm{8}\boldsymbol{\div}\mathrm{3}\right)×\mathrm{2} \\ $$$$\:\:\:\:\left(\mathrm{2}\right).\:\mathrm{2}\frac{\mathrm{5}}{\mathrm{3}}+\mathrm{3}\frac{\mathrm{2}}{\mathrm{4}} \\ $$

Question Number 82816 Answers: 0 Comments: 3

calculate the exact value ∫_0 ^∞ ((cos(x))/(x^2 +1)) dx

$${calculate}\:{the}\:{exact}\:{value}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{cos}\left({x}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx} \\ $$

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