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Question Number 97799 Answers: 0 Comments: 1

solve y^′ cosx +y sinx =cosx +sinx

$$\mathrm{solve}\:\mathrm{y}^{'} \mathrm{cosx}\:+\mathrm{y}\:\mathrm{sinx}\:=\mathrm{cosx}\:+\mathrm{sinx} \\ $$

Question Number 97798 Answers: 0 Comments: 0

solve y′′−y =xsin(2x)

$$\mathrm{solve}\:\mathrm{y}''−\mathrm{y}\:=\mathrm{xsin}\left(\mathrm{2x}\right) \\ $$

Question Number 97797 Answers: 3 Comments: 0

solve y^(′′) −y = x

$$\mathrm{solve}\:\mathrm{y}^{''} \:−\mathrm{y}\:=\:\mathrm{x} \\ $$

Question Number 97795 Answers: 1 Comments: 0

calculate Σ_(n=1) ^∞ (((−1)^(n−1) )/([(√n)])) [..] meant the floor

$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}−\mathrm{1}} }{\left[\sqrt{\mathrm{n}}\right]} \\ $$$$\left[..\right]\:\mathrm{meant}\:\mathrm{the}\:\mathrm{floor} \\ $$

Question Number 97794 Answers: 1 Comments: 3

solve y^(′′) +y =(1/(cosx))

$$\mathrm{solve}\:\mathrm{y}^{''} \:+\mathrm{y}\:=\frac{\mathrm{1}}{\mathrm{cosx}} \\ $$

Question Number 97784 Answers: 1 Comments: 0

If f(x)=((( x)^(1/2) )^(1/2) )^⋰ find: (dy/dx)

$${If}\:{f}\left({x}\right)=\left(\left(\left(\:{x}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \right)^{\frac{\mathrm{1}}{\mathrm{2}}} \right)^{\iddots} \\ $$$${find}:\:\frac{{dy}}{{dx}} \\ $$

Question Number 97782 Answers: 2 Comments: 1

Evaluate: ∫ ((sinx)/(1 +sin^2 x))dx

$${Evaluate}: \\ $$$$\int\:\frac{{sinx}}{\mathrm{1}\:+{sin}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 97781 Answers: 1 Comments: 0

Given the sequences (u_n )_(n∈N) and (v_n )_(n∈N) defined by u_n =Σ_(k=0) ^n (1/(k!)) and v_n =u_n +(1/(n(n!))) a\ Show that (u_n )_n is of Cauchy. Deduce that (u_n )_n converges. b\ Show that (u_n )_n and (v_n )_n are adjacent c\ Show that their common limit is not a rational number.

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{sequences}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} \:\mathrm{and}\:\left(\mathrm{v}_{\mathrm{n}} \right)_{\mathrm{n}\in\mathbb{N}} \mathrm{defined} \\ $$$$\mathrm{by}\:\mathrm{u}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{k}!}\:\mathrm{and}\:\mathrm{v}_{\mathrm{n}} =\mathrm{u}_{\mathrm{n}} +\frac{\mathrm{1}}{\mathrm{n}\left(\mathrm{n}!\right)} \\ $$$$\mathrm{a}\backslash\:\mathrm{Show}\:\mathrm{that}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}} \:\mathrm{is}\:\mathrm{of}\:\mathrm{Cauchy}.\:\mathcal{D}\mathrm{educe}\:\mathrm{that} \\ $$$$\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}} \:\mathrm{converges}. \\ $$$$\mathrm{b}\backslash\:\mathrm{Show}\:\mathrm{that}\:\left(\mathrm{u}_{\mathrm{n}} \right)_{\mathrm{n}} \:\mathrm{and}\:\left(\mathrm{v}_{\mathrm{n}} \right)_{\mathrm{n}} \:\mathrm{are}\:\mathrm{adjacent} \\ $$$$\mathrm{c}\backslash\:\mathrm{Show}\:\mathrm{that}\:\mathrm{their}\:\mathrm{common}\:\mathrm{limit}\:\mathrm{is}\:\mathrm{not}\:\mathrm{a}\:\mathrm{rational} \\ $$$$\mathrm{number}. \\ $$

Question Number 97779 Answers: 0 Comments: 1

Question Number 97775 Answers: 3 Comments: 2

Question Number 97759 Answers: 1 Comments: 0

∫ ((sin^5 (x) dx)/(√(cos (x)))) ?

$$\int\:\frac{\mathrm{sin}\:^{\mathrm{5}} \left({x}\right)\:{dx}}{\sqrt{\mathrm{cos}\:\left({x}\right)}}\:? \\ $$

Question Number 97752 Answers: 1 Comments: 4

Question Number 97751 Answers: 2 Comments: 3

(y^2 −xy)dx + 2xy dy = 0

$$\left(\mathrm{y}^{\mathrm{2}} −\mathrm{xy}\right)\mathrm{dx}\:+\:\mathrm{2xy}\:\mathrm{dy}\:=\:\mathrm{0}\: \\ $$

Question Number 97746 Answers: 1 Comments: 1

Determine all pairs (x,y) of integers satisfying 1+2^x +2^(2x+1) =y^2

$$\mathrm{Determine}\:\mathrm{all}\:\mathrm{pairs}\:\left(\mathrm{x},\mathrm{y}\right) \\ $$$$\mathrm{of}\:\mathrm{integers}\:\mathrm{satisfying}\:\mathrm{1}+\mathrm{2}^{\mathrm{x}} +\mathrm{2}^{\mathrm{2x}+\mathrm{1}} =\mathrm{y}^{\mathrm{2}} \: \\ $$

Question Number 97737 Answers: 2 Comments: 3

If ^((a^2 −a)) C_2 =^((a^2 −a)) C_4 , then a =

$$\mathrm{If}\:\:^{\left({a}^{\mathrm{2}} −{a}\right)} {C}_{\mathrm{2}} =\:^{\left({a}^{\mathrm{2}} −{a}\right)} {C}_{\mathrm{4}} \:,\:\mathrm{then}\:{a}\:= \\ $$

Question Number 97725 Answers: 0 Comments: 3

log _5 (4x)=log _(10) (x) find x ?

$$\mathrm{log}\:_{\mathrm{5}} \left(\mathrm{4x}\right)=\mathrm{log}\:_{\mathrm{10}} \left(\mathrm{x}\right) \\ $$$$\mathrm{find}\:\mathrm{x}\:? \\ $$

Question Number 97721 Answers: 1 Comments: 3

Question Number 97892 Answers: 1 Comments: 0

Question Number 97707 Answers: 3 Comments: 0

Question Number 97694 Answers: 1 Comments: 7

Question Number 97683 Answers: 3 Comments: 3

Evaluate ∫_0 ^1 (1/(√(16 + 9x^2 ))) dx

$$\:\mathrm{Evaluate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\sqrt{\mathrm{16}\:+\:\mathrm{9}{x}^{\mathrm{2}} }}\:{dx} \\ $$

Question Number 97680 Answers: 0 Comments: 1

Question Number 97675 Answers: 1 Comments: 0

Question Number 97671 Answers: 0 Comments: 1

Question Number 97660 Answers: 2 Comments: 1

Question Number 97658 Answers: 0 Comments: 1

The value of cos ((2π)/7) +cos ((4π)/7)+cos ((6π)/7) is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{7}}\:+\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{7}}+\mathrm{cos}\:\frac{\mathrm{6}\pi}{\mathrm{7}}\:\:\mathrm{is} \\ $$

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