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Question Number 87723 Answers: 1 Comments: 0

∫((1/(x−1))+((Σ_(k=0) ^(2018) (k+1)x^k )/(Σ_(k=0) ^(2019) x^k )))dx

$$\int\left(\frac{\mathrm{1}}{{x}−\mathrm{1}}+\frac{\underset{{k}=\mathrm{0}} {\overset{\mathrm{2018}} {\sum}}\left({k}+\mathrm{1}\right){x}^{{k}} }{\underset{{k}=\mathrm{0}} {\overset{\mathrm{2019}} {\sum}}{x}^{{k}} }\right){dx} \\ $$

Question Number 87716 Answers: 1 Comments: 1

Question Number 87711 Answers: 1 Comments: 2

∫_0 ^∞ ((1−xe^(−x) −e^(−x) )/(x(e^x −e^(−x) )))dx

$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}−{xe}^{−{x}} −{e}^{−{x}} }{{x}\left({e}^{{x}} −{e}^{−{x}} \right)}{dx} \\ $$

Question Number 87709 Answers: 0 Comments: 0

sbow that ∫_1 ^∞ (([3x])/(([x])!))dx=4e−1

$${sbow}\:{that} \\ $$$$\int_{\mathrm{1}} ^{\infty} \frac{\left[\mathrm{3}{x}\right]}{\left(\left[{x}\right]\right)!}{dx}=\mathrm{4}{e}−\mathrm{1} \\ $$

Question Number 87692 Answers: 0 Comments: 8

sir Ma?h+t?que you have posted ∫(dx/(((x+1)....(x+n))^2 ))=......can you reposted it please

$${sir}\:{Ma}?{h}+{t}?{que}\:{you}\:{have}\:{posted} \\ $$$$\int\frac{{dx}}{\left(\left({x}+\mathrm{1}\right)....\left({x}+{n}\right)\right)^{\mathrm{2}} }=......{can}\:{you}\:{reposted}\:{it}\:{please} \\ $$

Question Number 87690 Answers: 1 Comments: 4

lim_(x→0) ((2sin x−sin 2x)/(x−sin x))

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

Question Number 87687 Answers: 1 Comments: 0

Let w=[1;(π/n)] ,n∈N^∗ a_n =Σ_(p=0) ^(n−1) ((2p+1)/(1−w^(2p+1) )) and b_n =Σ_(p=0) ^(n−1) (n/(1+w^p )) Find all integer n such as a_n =b_n

$${Let}\:\:{w}=\left[\mathrm{1};\frac{\pi}{{n}}\right]\:,{n}\in\mathbb{N}^{\ast} \: \\ $$$$\:{a}_{{n}} =\underset{{p}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}\:\frac{\mathrm{2}{p}+\mathrm{1}}{\mathrm{1}−{w}^{\mathrm{2}{p}+\mathrm{1}} }\:\:\:\:{and}\:\:\:{b}_{{n}} =\underset{{p}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}\:\frac{{n}}{\mathrm{1}+{w}^{{p}} }\: \\ $$$${Find}\:\:{all}\:{integer}\:{n}\:{such}\:{as}\:\:{a}_{{n}} ={b}_{{n}} \: \\ $$

Question Number 87686 Answers: 3 Comments: 0

∫(√((ln(x+(√(1+x^2 ))))/(1+x^2 ))) dx

$$\int\sqrt{\frac{{ln}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)}{\mathrm{1}+{x}^{\mathrm{2}} }}\:{dx} \\ $$

Question Number 87682 Answers: 0 Comments: 0

what is ▽^2 ((1/r^→ )) if ▽^→ = i^ (∂/∂x)+j^ (∂/∂y)+k^ (∂/∂z) and r^→ = i^ x + j^ y + k^ z

$$\mathrm{what}\:\mathrm{is}\:\bigtriangledown^{\mathrm{2}} \left(\frac{\mathrm{1}}{\overset{\rightarrow} {\mathrm{r}}}\right)\:\mathrm{if}\: \\ $$$$\overset{\rightarrow} {\bigtriangledown}\:=\:\hat {\mathrm{i}}\:\frac{\partial}{\partial\mathrm{x}}+\hat {\mathrm{j}}\frac{\partial}{\partial\mathrm{y}}+\hat {\mathrm{k}}\:\frac{\partial}{\partial\mathrm{z}} \\ $$$$\mathrm{and}\:\overset{\rightarrow} {\mathrm{r}}\:=\:\hat {\mathrm{i}x}\:+\:\hat {\mathrm{j}y}\:+\:\hat {\mathrm{k}z}\: \\ $$

Question Number 87671 Answers: 1 Comments: 3

Question Number 87669 Answers: 1 Comments: 4

∫_2 ^( e) ((1/(ln x))−(1/(ln^2 x))) dx?

$$\int_{\mathrm{2}} ^{\:\:\mathrm{e}} \left(\frac{\mathrm{1}}{\mathrm{ln}\:\mathrm{x}}−\frac{\mathrm{1}}{\mathrm{ln}^{\mathrm{2}} \mathrm{x}}\right)\:\mathrm{dx}? \\ $$

Question Number 87648 Answers: 0 Comments: 4

the sequence a_1 ,a_2 ,a_3 , ... satisfies the relation a_(n+1) = a_n +a_(n−1) , for n>1. given that a_(20) = 6765 and a_(18) = 2584 what is a_(16)

$$\mathrm{the}\:\mathrm{sequence}\:\mathrm{a}_{\mathrm{1}} ,\mathrm{a}_{\mathrm{2}} ,\mathrm{a}_{\mathrm{3}} ,\:...\:\mathrm{satisfies} \\ $$$$\mathrm{the}\:\mathrm{relation}\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:=\:\mathrm{a}_{\mathrm{n}} +\mathrm{a}_{\mathrm{n}−\mathrm{1}} \:,\:\mathrm{for} \\ $$$$\mathrm{n}>\mathrm{1}.\:\mathrm{given}\:\mathrm{that}\:\mathrm{a}_{\mathrm{20}} \:=\:\mathrm{6765}\:\mathrm{and} \\ $$$$\mathrm{a}_{\mathrm{18}} \:=\:\mathrm{2584}\:\mathrm{what}\:\mathrm{is}\:\mathrm{a}_{\mathrm{16}} \\ $$

Question Number 87647 Answers: 1 Comments: 0

If a_1 = 1 , a_(n+1 ) = 2a_n + 5 , n = 1,2,3,.... then a_(100) = ?

$$\mathrm{If}\:\mathrm{a}_{\mathrm{1}} \:=\:\mathrm{1}\:,\:\mathrm{a}_{\mathrm{n}+\mathrm{1}\:} =\:\mathrm{2a}_{\mathrm{n}} \:+\:\mathrm{5}\:,\:\mathrm{n}\:=\: \\ $$$$\mathrm{1},\mathrm{2},\mathrm{3},....\:\mathrm{then}\:\mathrm{a}_{\mathrm{100}} \:=\:? \\ $$

Question Number 87656 Answers: 1 Comments: 3

((1+sin((1/8))π+i cos((1/8))π)/(1+sin((1/8))π−i cos((1/8))π))=?

$$\frac{\mathrm{1}+{sin}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi+{i}\:{cos}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi}{\mathrm{1}+{sin}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi−{i}\:{cos}\left(\frac{\mathrm{1}}{\mathrm{8}}\right)\pi}=? \\ $$

Question Number 87643 Answers: 0 Comments: 0

Given a random variable X of image set X(Ω)=[1;−1;2] with probabilities P(X=1)=e^a , P(X=−1)=e^b , and P(X=2)=e^c where a, b, and c are in an Arithmetic Progression. Assuming the mathematical expection E(X) of X is equal to 1. 1∙ Suppose the common difference of the Arithmetic Progression is r a∙ Determine the exact values of the real numbers a, b, and c. b. Show that the variance V(X) of X is equal to ((22)/7).

$${Given}\:{a}\:{random}\:{variable}\:\boldsymbol{{X}}\:{of}\:{image}\:{set} \\ $$$${X}\left(\Omega\right)=\left[\mathrm{1};−\mathrm{1};\mathrm{2}\right]\:{with}\:{probabilities}\:{P}\left({X}=\mathrm{1}\right)={e}^{{a}} , \\ $$$${P}\left({X}=−\mathrm{1}\right)={e}^{{b}} ,\:{and}\:{P}\left({X}=\mathrm{2}\right)={e}^{{c}} \:{where}\:{a},\:{b},\:{and}\:{c}\: \\ $$$${are}\:{in}\:\:{an}\:{Arithmetic}\:{Progression}. \\ $$$${Assuming}\:{the}\:{mathematical}\:{expection}\:{E}\left({X}\right)\:{of}\:{X}\: \\ $$$${is}\:{equal}\:{to}\:\mathrm{1}. \\ $$$$\mathrm{1}\centerdot\:{Suppose}\:{the}\:{common}\:{difference}\:{of}\:{the}\:{Arithmetic}\:{Progression}\:{is}\:\boldsymbol{{r}} \\ $$$$\boldsymbol{{a}}\centerdot\:{Determine}\:{the}\:{exact}\:{values}\:{of}\:{the}\:{real}\:{numbers}\:{a},\:{b},\:{and}\:{c}. \\ $$$$\boldsymbol{{b}}.\:{Show}\:{that}\:{the}\:{variance}\:{V}\left({X}\right)\:{of}\:{X}\:{is}\:{equal}\:{to}\:\frac{\mathrm{22}}{\mathrm{7}}. \\ $$$$ \\ $$$$ \\ $$

Question Number 87637 Answers: 1 Comments: 0

((∣x−3∣^(x+1) ))^(1/(4 )) = ((∣x−3∣^(x−2) ))^(1/(3 ))

$$\sqrt[{\mathrm{4}\:\:}]{\mid\mathrm{x}−\mathrm{3}\mid^{\mathrm{x}+\mathrm{1}} }\:=\:\sqrt[{\mathrm{3}\:\:}]{\mid\mathrm{x}−\mathrm{3}\mid^{\mathrm{x}−\mathrm{2}} } \\ $$

Question Number 87625 Answers: 2 Comments: 0

if f(x)=sin^(−1) (cos[x]) find Df and Rf the function notice/ [...] is floor

$${if}\:{f}\left({x}\right)={sin}^{−\mathrm{1}} \left({cos}\left[{x}\right]\right) \\ $$$${find}\:{Df}\:{and}\:\:{Rf}\:{the}\:{function} \\ $$$$ \\ $$$${notice}/\:\left[...\right]\:{is}\:{floor} \\ $$

Question Number 87624 Answers: 0 Comments: 1

find minimum value of cos^2 w + sec^2 w

$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{w}\:+ \\ $$$$\mathrm{sec}\:^{\mathrm{2}} \mathrm{w}\: \\ $$

Question Number 87614 Answers: 1 Comments: 0

{ (((x+y).2^(y−2x) =6.25)),(((x+y)^(1/(2x−y)) =5)) :}

$$\begin{cases}{\left({x}+{y}\right).\mathrm{2}^{{y}−\mathrm{2}{x}} =\mathrm{6}.\mathrm{25}}\\{\left({x}+{y}\right)^{\frac{\mathrm{1}}{\mathrm{2}{x}−{y}}} =\mathrm{5}}\end{cases} \\ $$

Question Number 87613 Answers: 1 Comments: 1

Question Number 87630 Answers: 0 Comments: 1

Question Number 87598 Answers: 0 Comments: 1

Question Number 87586 Answers: 1 Comments: 0

l.c.m of two numbers is p^2 q^4 r^4 p q r are primes.find the possible no. of pairs

$${l}.{c}.{m}\:{of}\:{two}\:{numbers}\:{is}\:{p}^{\mathrm{2}} {q}^{\mathrm{4}} {r}^{\mathrm{4}} \:{p}\:{q}\:{r}\:{are} \\ $$$${primes}.{find}\:{the}\:{possible}\:{no}.\:{of}\:{pairs} \\ $$

Question Number 87585 Answers: 1 Comments: 0

Question Number 87581 Answers: 2 Comments: 1

Question Number 110350 Answers: 2 Comments: 0

((bob)/(hans)) (1)lim_(x→3) ((sin (x−(9/x)))/(tan (x−3)cos ((9/x)−x)))= (2)(x tan^(−1) (y))dx +( (x^2 /(2(1+y^2 )))). dy =0

$$\:\:\:\frac{{bob}}{{hans}} \\ $$$$\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left({x}−\frac{\mathrm{9}}{{x}}\right)}{\mathrm{tan}\:\left({x}−\mathrm{3}\right)\mathrm{cos}\:\left(\frac{\mathrm{9}}{{x}}−{x}\right)}= \\ $$$$\left(\mathrm{2}\right)\left({x}\:\mathrm{tan}^{−\mathrm{1}} \left({y}\right)\right){dx}\:+\left(\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}\left(\mathrm{1}+{y}^{\mathrm{2}} \right)}\right).\:{dy}\:=\mathrm{0}\: \\ $$

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