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Question Number 83477 Answers: 0 Comments: 1

a^b +b^a =1 a=? , b=? a≠b≠0

$${a}^{{b}} +{b}^{{a}} =\mathrm{1}\:\:\:{a}=?\:,\:{b}=? \\ $$$${a}\neq{b}\neq\mathrm{0} \\ $$

Question Number 83473 Answers: 1 Comments: 0

solve in R sin(πln(x))+cos(πln(x))=1

$${solve}\:{in}\:{R} \\ $$$${sin}\left(\pi{ln}\left({x}\right)\right)+{cos}\left(\pi{ln}\left({x}\right)\right)=\mathrm{1} \\ $$

Question Number 83471 Answers: 2 Comments: 1

Question Number 83459 Answers: 0 Comments: 2

Question Number 83445 Answers: 2 Comments: 1

The nearest distance of (0, 3) to curve : y = 6 − x^2 is ...

$${The}\:\:{nearest}\:\:{distance}\:\:{of}\:\:\left(\mathrm{0},\:\mathrm{3}\right)\:\:{to}\:\:{curve}\:\::\:\:{y}\:=\:\:\mathrm{6}\:−\:{x}^{\mathrm{2}} \:\:{is}\:\:... \\ $$

Question Number 83441 Answers: 1 Comments: 0

calculate ∫_0 ^(π/4) (√(1+2tanx))dx

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \sqrt{\mathrm{1}+\mathrm{2}{tanx}}{dx} \\ $$

Question Number 83440 Answers: 0 Comments: 0

find ∫_0 ^(π/2) (dx/(sinx^(cosx) +cosx^(sinx) ))

$${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{dx}}{{sinx}^{{cosx}} +{cosx}^{{sinx}} } \\ $$

Question Number 83430 Answers: 1 Comments: 0

prove that? sin 3θ sin^3 θ + cos 3θ cos^3 θ = cos^3 (2θ)

$$\mathrm{prove}\:\mathrm{that}? \\ $$$$\mathrm{sin}\:\mathrm{3}\theta\:\mathrm{sin}^{\mathrm{3}} \:\theta\:+\:\mathrm{cos}\:\mathrm{3}\theta\:\mathrm{cos}\:^{\mathrm{3}} \theta\:=\:\: \\ $$$$\mathrm{cos}\:^{\mathrm{3}} \:\left(\mathrm{2}\theta\right) \\ $$

Question Number 83425 Answers: 0 Comments: 1

((tan 3a)/(tan a)) = k show that ((sin 3a)/(sin a)) = ((2k)/(k−1))

$$\frac{\mathrm{tan}\:\mathrm{3a}}{\mathrm{tan}\:\mathrm{a}}\:=\:\mathrm{k} \\ $$$$\mathrm{show}\:\mathrm{that}\:\frac{\mathrm{sin}\:\mathrm{3a}}{\mathrm{sin}\:\mathrm{a}}\:=\:\frac{\mathrm{2k}}{\mathrm{k}−\mathrm{1}} \\ $$

Question Number 83492 Answers: 0 Comments: 0

f(x)= (1/(2(√x))) lim_(t→0) ((f(2x−t)+f(2x−2t)−2f(2x+t))/t)

$$\mathrm{f}\left(\mathrm{x}\right)=\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{x}}} \\ $$$$\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{f}\left(\mathrm{2x}−\mathrm{t}\right)+\mathrm{f}\left(\mathrm{2x}−\mathrm{2t}\right)−\mathrm{2f}\left(\mathrm{2x}+\mathrm{t}\right)}{\mathrm{t}} \\ $$

Question Number 83491 Answers: 0 Comments: 1

f(x) = (((√(1+sin (2x)))−(√(1−2sin (x))))/x) g(x) = 2x+(√(2x)) find lim_(x→0) g(f(x))

$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\sqrt{\mathrm{1}+\mathrm{sin}\:\left(\mathrm{2x}\right)}−\sqrt{\mathrm{1}−\mathrm{2sin}\:\left(\mathrm{x}\right)}}{\mathrm{x}} \\ $$$$\mathrm{g}\left(\mathrm{x}\right)\:=\:\mathrm{2x}+\sqrt{\mathrm{2x}} \\ $$$$\mathrm{find}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{g}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\: \\ $$

Question Number 83420 Answers: 1 Comments: 4

find range x of function x−4(√y) = 2(√(x−y))

$$\mathrm{find}\:\mathrm{range}\:\mathrm{x}\:\mathrm{of}\:\mathrm{function}\: \\ $$$$\mathrm{x}−\mathrm{4}\sqrt{\mathrm{y}}\:=\:\mathrm{2}\sqrt{\mathrm{x}−\mathrm{y}} \\ $$

Question Number 83413 Answers: 1 Comments: 3

y = x ∣x∣ find y ′ ?

$$\mathrm{y}\:=\:\mathrm{x}\:\mid\mathrm{x}\mid \\ $$$$\mathrm{find}\:\mathrm{y}\:'\:? \\ $$

Question Number 83411 Answers: 2 Comments: 1

Question Number 83406 Answers: 3 Comments: 3

If u_1 +u_2 +u_3 +...+u_n = 2n^2 +n is a AP. find the value of u_1 +u_2 +u_3 +...+u_(2n−2) +u_(2n−1) .

$$\mathrm{If}\:\mathrm{u}_{\mathrm{1}} +\mathrm{u}_{\mathrm{2}} +\mathrm{u}_{\mathrm{3}} +...+\mathrm{u}_{\mathrm{n}} \:=\:\mathrm{2n}^{\mathrm{2}} +\mathrm{n}\: \\ $$$$\mathrm{is}\:\mathrm{a}\:\:\mathrm{AP}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\mathrm{u}_{\mathrm{1}} +\mathrm{u}_{\mathrm{2}} +\mathrm{u}_{\mathrm{3}} +...+\mathrm{u}_{\mathrm{2n}−\mathrm{2}} +\mathrm{u}_{\mathrm{2n}−\mathrm{1}} \:. \\ $$

Question Number 83405 Answers: 0 Comments: 2

lim_(b→1^− ) ∫_0 ^b ((sin (x))/(√(1−x^2 ))) dx ?

$$\underset{\mathrm{b}\rightarrow\mathrm{1}^{−} } {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\mathrm{b}} \:\frac{\mathrm{sin}\:\left(\mathrm{x}\right)}{\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:?\: \\ $$

Question Number 83403 Answers: 1 Comments: 0

what is range function y = (1/((x−1)^2 ))

$$\mathrm{what}\:\mathrm{is}\:\mathrm{range}\:\mathrm{function}\: \\ $$$$\mathrm{y}\:=\:\frac{\mathrm{1}}{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 83401 Answers: 0 Comments: 2

lim_(x→∞) (6−8xsin ((3/x)))= ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{6}−\mathrm{8xsin}\:\left(\frac{\mathrm{3}}{\mathrm{x}}\right)\right)=\:? \\ $$

Question Number 83395 Answers: 0 Comments: 0

Let R be a relation such that R = {3,6,12,24} prove that R is a strict order relation.

$$\mathrm{Let}\:\mathrm{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{relation}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{R}\:=\:\left\{\mathrm{3},\mathrm{6},\mathrm{12},\mathrm{24}\right\} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{R}\:\mathrm{is}\:\mathrm{a}\:\mathrm{strict}\:\mathrm{order} \\ $$$$\mathrm{relation}.\: \\ $$

Question Number 83385 Answers: 2 Comments: 1

∫((1+ae^(−(a+1)x) +(a+1)e^(−ax) )/x^2 ) dx, a∈z^+

$$\int\frac{\mathrm{1}+{ae}^{−\left({a}+\mathrm{1}\right){x}} +\left({a}+\mathrm{1}\right){e}^{−{ax}} }{{x}^{\mathrm{2}} }\:{dx},\:\:{a}\in{z}^{+} \\ $$

Question Number 83383 Answers: 1 Comments: 0

find ∫_0 ^2 ∫_0 ^(√(4−x^2 )) ∫_0 ^(2−z) zdxdydz pleas help me sir

$${find}\:\int_{\mathrm{0}} ^{\mathrm{2}} \int_{\mathrm{0}} ^{\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }} \int_{\mathrm{0}} ^{\mathrm{2}−{z}} {zdxdydz} \\ $$$${pleas}\:{help}\:{me}\:{sir} \\ $$

Question Number 83381 Answers: 0 Comments: 0

Given that the function f(x) = x^3 is differentiable in the interval (−2,2) us the mean value theorem to find the value of x for which the tangent to the curve is parrallel to the chord through the points (−2,8) and (2,8).

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function}\:{f}\left({x}\right)\:=\:{x}^{\mathrm{3}} \:\mathrm{is}\: \\ $$$$\mathrm{differentiable}\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval}\:\left(−\mathrm{2},\mathrm{2}\right)\:\mathrm{us}\:\mathrm{the}\:\mathrm{mean} \\ $$$$\mathrm{value}\:\mathrm{theorem}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\: \\ $$$$\mathrm{tangent}\:\mathrm{to}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{is}\:\mathrm{parrallel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{chord}\: \\ $$$$\mathrm{through}\:\mathrm{the}\:\mathrm{points}\:\left(−\mathrm{2},\mathrm{8}\right)\:\mathrm{and}\:\left(\mathrm{2},\mathrm{8}\right). \\ $$

Question Number 83378 Answers: 0 Comments: 2

x+y+z=1 x^2 +y^2 +z^2 =2 x^3 +y^3 +z^3 =3 find x^4 +y^4 +z^4 =?

$${x}+{y}+{z}=\mathrm{1} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{2} \\ $$$${x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} =\mathrm{3} \\ $$$${find} \\ $$$${x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} =? \\ $$

Question Number 83373 Answers: 0 Comments: 4

Question Number 83372 Answers: 0 Comments: 1

Question Number 83370 Answers: 0 Comments: 3

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