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Question Number 207565 Answers: 2 Comments: 0

find ∫_0 ^(π/2) (x^2 /(tan^2 x))dx

$${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{x}^{\mathrm{2}} }{{tan}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 207533 Answers: 2 Comments: 1

Question Number 207528 Answers: 2 Comments: 0

Question Number 207519 Answers: 1 Comments: 0

Find: lim_(x→2^− ) (((x + 2)∙(x + 1))/(∣x + 2∣)) = ?

$$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{2}^{−} } {\mathrm{lim}}\:\:\frac{\left(\mathrm{x}\:+\:\mathrm{2}\right)\centerdot\left(\mathrm{x}\:+\:\mathrm{1}\right)}{\mid\mathrm{x}\:+\:\mathrm{2}\mid}\:\:=\:\:? \\ $$

Question Number 207518 Answers: 1 Comments: 0

cosx cos3x = cos5x cos7x ⇒ x = ?

$$\mathrm{cos}\boldsymbol{\mathrm{x}}\:\mathrm{cos3}\boldsymbol{\mathrm{x}}\:\:=\:\:\mathrm{cos5}\boldsymbol{\mathrm{x}}\:\mathrm{cos7}\boldsymbol{\mathrm{x}} \\ $$$$\Rightarrow\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 207516 Answers: 2 Comments: 1

3(sinθ − cosθ)^4 + 6(sinθ + cosθ)^2 + 4(sin^6 θ + cos^6 θ) = ?

$$\mathrm{3}\left(\mathrm{sin}\theta\:−\:\mathrm{cos}\theta\right)^{\mathrm{4}} \:+\:\mathrm{6}\left(\mathrm{sin}\theta\:+\:\mathrm{cos}\theta\right)^{\mathrm{2}} \\ $$$$+\:\mathrm{4}\left(\mathrm{sin}^{\mathrm{6}} \theta\:+\:\mathrm{cos}^{\mathrm{6}} \theta\right)\:=\:? \\ $$

Question Number 207509 Answers: 1 Comments: 0

Question Number 207502 Answers: 2 Comments: 0

(6/(∣x − 4∣ − 3)) ≥ 1

$$\frac{\mathrm{6}}{\mid\boldsymbol{\mathrm{x}}\:−\:\mathrm{4}\mid\:−\:\mathrm{3}}\:\:\geqslant\:\:\mathrm{1} \\ $$

Question Number 207498 Answers: 1 Comments: 0

cos2x + sinx = tg(225°)∙(0,360°) sum of roots = ?

$$\mathrm{cos2}\boldsymbol{\mathrm{x}}\:+\:\mathrm{sin}\boldsymbol{\mathrm{x}}\:=\:\mathrm{tg}\left(\mathrm{225}°\right)\centerdot\left(\mathrm{0},\mathrm{360}°\right) \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{roots}\:=\:? \\ $$

Question Number 207493 Answers: 2 Comments: 0

lim_(n→∞) (((n − 1)/(n + 2)))^(n+3) = ?

$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{n}\:−\:\mathrm{1}}{\mathrm{n}\:+\:\mathrm{2}}\right)^{\boldsymbol{\mathrm{n}}+\mathrm{3}} \:=\:\:? \\ $$

Question Number 207482 Answers: 1 Comments: 0

Question Number 207477 Answers: 0 Comments: 8

is there any generale form for this sequense { ((u_(n+1) =((au_n +b)/(cu_n +d)))),((u_m =k)) :} I need u_n in terms of n i have try to derrive it for a long time but i cant

$${is}\:{there}\:{any}\:{generale}\:{form}\:{for}\:{this}\:{sequense}\: \\ $$$$\begin{cases}{{u}_{{n}+\mathrm{1}} =\frac{{au}_{{n}} +{b}}{{cu}_{{n}} +{d}}}\\{{u}_{{m}} ={k}}\end{cases} \\ $$$${I}\:{need}\:{u}_{{n}} \:{in}\:{terms}\:{of}\:{n}\:{i}\:{have}\:{try}\:{to}\:{derrive}\:{it}\:{for}\:{a}\:{long}\:{time}\:{but}\:{i}\:{cant} \\ $$

Question Number 207724 Answers: 1 Comments: 0

2 tg^3 x − 2 tg^2 x + 6 tg x = 3 , [0 ; 2𝛑] Sum of roots = ?

$$\mathrm{2}\:\mathrm{tg}^{\mathrm{3}} \:\boldsymbol{\mathrm{x}}\:−\:\mathrm{2}\:\mathrm{tg}^{\mathrm{2}} \:\boldsymbol{\mathrm{x}}\:+\:\mathrm{6}\:\mathrm{tg}\:\boldsymbol{\mathrm{x}}\:=\:\mathrm{3}\:\:\:,\:\:\:\left[\mathrm{0}\:;\:\mathrm{2}\boldsymbol{\pi}\right] \\ $$$$\mathrm{Sum}\:\mathrm{of}\:\mathrm{roots}\:=\:? \\ $$

Question Number 207723 Answers: 0 Comments: 2

lim∫_0 ^∞ (1−e^(−ncos(x)) )dx

$$\mathrm{li}{m}\int_{\mathrm{0}} ^{\infty} \left(\mathrm{1}−{e}^{−{ncos}\left({x}\right)} \right){dx} \\ $$

Question Number 207466 Answers: 2 Comments: 0

Question Number 207463 Answers: 1 Comments: 0

1 − sin^2 x = (√2) find: x = ?

$$\mathrm{1}\:−\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{x}\:=\:\sqrt{\mathrm{2}}\:\:\:\:\:\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 207462 Answers: 0 Comments: 1

4 sin (x/2) = 1 find: x = ?

$$\mathrm{4}\:\mathrm{sin}\:\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\:=\:\mathrm{1}\:\:\:\:\:\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 207461 Answers: 0 Comments: 2

Question Number 207458 Answers: 0 Comments: 2

Question Number 207487 Answers: 1 Comments: 0

∣x^2 − 3x − 4∣ = ∣x − 4∣ find: min and max = ?

$$\mid\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{3x}\:−\:\mathrm{4}\mid\:=\:\mid\mathrm{x}\:−\:\mathrm{4}\mid \\ $$$$\mathrm{find}:\:\:\:\boldsymbol{\mathrm{min}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{max}}\:\:=\:\:? \\ $$

Question Number 207486 Answers: 2 Comments: 2

Question Number 207456 Answers: 0 Comments: 0

Question Number 207455 Answers: 0 Comments: 0

Question Number 207450 Answers: 1 Comments: 0

Find the relation between m and n for which the following holds ((d(y))/(d(x)))∣_(x=n) =(((d(x))/(d(y)))∣_(y=m) )^(−1)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{relation}\:\mathrm{between}\:{m}\:\mathrm{and}\:{n}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{following}\:\:\mathrm{holds} \\ $$$$\:\frac{{d}\left({y}\right)}{{d}\left({x}\right)}\mid_{{x}={n}} =\left(\frac{{d}\left({x}\right)}{{d}\left({y}\right)}\mid_{{y}={m}} \right)^{−\mathrm{1}} \\ $$

Question Number 207451 Answers: 0 Comments: 0

find the volume in the first quadrant of the solid obtained by rotating the region bounded by the curves x = sinh(y) , x = cosh(y) about y axis (use washer method) ?

$${find}\:{the}\:{volume}\:{in}\:{the}\:{first}\:{quadrant} \\ $$$$\:{of}\:{the}\:{solid}\:{obtained}\:{by}\:{rotating} \\ $$$${the}\:{region}\:{bounded}\:{by}\:{the}\:{curves}\: \\ $$$${x}\:=\:{sinh}\left({y}\right)\:,\:{x}\:=\:{cosh}\left({y}\right)\:{about}\:{y}\:{axis}\:\left({use}\:{washer}\:{method}\right)\:? \\ $$

Question Number 207442 Answers: 1 Comments: 3

If y=f(x), (d^2 x/dy^2 )=e^(y+1) , and the tangent line to the curve of the function f(x) on the point (x_1 ,−1) is paralel to the straight line g(x)=x−3, then find f′(x).

$$\mathrm{If}\:{y}={f}\left({x}\right),\:\frac{{d}^{\mathrm{2}} {x}}{{dy}^{\mathrm{2}} }={e}^{{y}+\mathrm{1}} ,\:\mathrm{and}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{line}\:\mathrm{to}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:{f}\left({x}\right)\:\mathrm{on}\:\mathrm{the}\:\mathrm{point} \\ $$$$\left({x}_{\mathrm{1}} ,−\mathrm{1}\right)\:\mathrm{is}\:\mathrm{paralel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{straight}\:\mathrm{line}\:{g}\left({x}\right)={x}−\mathrm{3},\:\mathrm{then}\:\mathrm{find}\:{f}'\left({x}\right). \\ $$

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