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Question Number 79964    Answers: 0   Comments: 3

∫(tan^2 x+tan^4 x)dx=[tan^2 x=t]=∫(t^2 +t^4 )dx=(t^3 /3)+(t^5 /5)+c

$$\int\left(\mathrm{tan}\:^{\mathrm{2}} {x}+\mathrm{tan}\:^{\mathrm{4}} {x}\right){dx}=\left[\mathrm{tan}\:^{\mathrm{2}} {x}={t}\right]=\int\left({t}^{\mathrm{2}} +{t}^{\mathrm{4}} \right){dx}=\frac{{t}^{\mathrm{3}} }{\mathrm{3}}+\frac{{t}^{\mathrm{5}} }{\mathrm{5}}+{c} \\ $$

Question Number 79947    Answers: 0   Comments: 4

Find ((ln 2)/(2!))+((ln 3)/(3!))+((ln 4)/(4!))+...+((ln n)/(n!))+...=?

$${Find} \\ $$$$\frac{\mathrm{ln}\:\mathrm{2}}{\mathrm{2}!}+\frac{\mathrm{ln}\:\mathrm{3}}{\mathrm{3}!}+\frac{\mathrm{ln}\:\mathrm{4}}{\mathrm{4}!}+...+\frac{\mathrm{ln}\:{n}}{{n}!}+...=? \\ $$

Question Number 79946    Answers: 2   Comments: 0

Find ∫_0 ^( n) [(x)^(1/3) ]dx=? in terms of n. (n∈N)

$${Find}\: \\ $$$$\int_{\mathrm{0}} ^{\:{n}} \left[\sqrt[{\mathrm{3}}]{{x}}\right]{dx}=?\: \\ $$$${in}\:{terms}\:{of}\:{n}.\:\left({n}\in\mathbb{N}\right) \\ $$

Question Number 79943    Answers: 1   Comments: 5

Question Number 79869    Answers: 0   Comments: 1

For witch value of α the integral I=∫_0 ^∞ ((1/(√(1+2x^2 )))−(α/(1+x)))dx converge; and in this case calculate α

$${For}\:\:{witch}\:\:{value}\:\:{of}\:\:\alpha\:\:{the}\:\:{integral} \\ $$$$\:\:{I}=\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{1}}{\sqrt{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }}−\frac{\alpha}{\mathrm{1}+{x}}\right){dx}\:\:{converge}; \\ $$$$\:\:{and}\:\:{in}\:\:{this}\:\:{case}\:\:{calculate}\:\:\alpha \\ $$

Question Number 79866    Answers: 0   Comments: 1

Chapter (2) Remainder Theorem and Factor Theorem Exercises(2.1) Remainder Throrem 1.Find the remainder when x^(8 ) +2x−5 is divided by (x−1). 2.Find the remainder when 2x^2 13x+10 is divided by (x−3).

$${Chapter}\:\left(\mathrm{2}\right) \\ $$$${Remainder}\:{Theorem} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{and} \\ $$$${Factor}\:{Theorem} \\ $$$${Exercises}\left(\mathrm{2}.\mathrm{1}\right) \\ $$$$\boldsymbol{\mathrm{Remainder}}\:\mathrm{T}\boldsymbol{\mathrm{hrorem}} \\ $$$$\mathrm{1}.\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:\boldsymbol{\mathrm{x}}^{\mathrm{8}\:} +\mathrm{2}\boldsymbol{\mathrm{x}}−\mathrm{5} \\ $$$$\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{1}\right). \\ $$$$\mathrm{2}.\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:\mathrm{2x}^{\mathrm{2}} \:\mathrm{13x}+\mathrm{10} \\ $$$$\mathrm{is}\:\mathrm{divided}\:\mathrm{by}\:\left(\mathrm{x}−\mathrm{3}\right). \\ $$

Question Number 79864    Answers: 0   Comments: 0

Question Number 79861    Answers: 0   Comments: 1

Question Number 79856    Answers: 0   Comments: 2

Question Number 79838    Answers: 1   Comments: 0

$$\because \\ $$

Question Number 79837    Answers: 1   Comments: 10

Question Number 79826    Answers: 0   Comments: 7

Question Number 79825    Answers: 0   Comments: 4

∫_( 0) ^( 1) (√(x^3 + 1)) dx

$$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\sqrt{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{1}}\:\:\mathrm{dx} \\ $$

Question Number 79824    Answers: 2   Comments: 7

Question Number 79816    Answers: 1   Comments: 0

hello mister. i need help explaining how determine the range of function of rational functions like (i) f(x)=((ax^2 +bx+c)/(px^2 +qx+r)) (ii) f(x)=((ax^2 +bx+c)/(px+q))

$$\mathrm{hello}\:\mathrm{mister}. \\ $$$$\mathrm{i}\:\mathrm{need}\:\mathrm{help}\:\mathrm{explaining}\:\mathrm{how}\:\mathrm{determine} \\ $$$$\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{function} \\ $$$$\mathrm{of}\:\mathrm{rational}\:\mathrm{functions} \\ $$$$\mathrm{like}\:\left(\mathrm{i}\right)\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}}{\mathrm{px}^{\mathrm{2}} +\mathrm{qx}+\mathrm{r}} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}}{\mathrm{px}+\mathrm{q}} \\ $$

Question Number 79814    Answers: 0   Comments: 5

Question Number 79807    Answers: 2   Comments: 2

Question Number 79798    Answers: 0   Comments: 7

Question Number 79794    Answers: 1   Comments: 2

Question Number 79792    Answers: 1   Comments: 1

JUST FOR FUN (1/2), (2/3), 1, (8/5), (8/3), ? what do you think is the next number ? why?

$${JUST}\:{FOR}\:{FUN} \\ $$$$ \\ $$$$\frac{\mathrm{1}}{\mathrm{2}},\:\frac{\mathrm{2}}{\mathrm{3}},\:\mathrm{1},\:\frac{\mathrm{8}}{\mathrm{5}},\:\frac{\mathrm{8}}{\mathrm{3}},\:? \\ $$$${what}\:{do}\:{you}\:{think}\:{is}\:{the}\:{next}\:{number}\:? \\ $$$${why}? \\ $$

Question Number 79766    Answers: 1   Comments: 0

what is x 2^x =(1+tan 0.01^o )(1+tan 0.02^o ) (1+tan 0.03^o )...(1+tan 44.99^o )

$$\mathrm{what}\:\mathrm{is}\:\mathrm{x} \\ $$$$\mathrm{2}^{\mathrm{x}} =\left(\mathrm{1}+\mathrm{tan}\:\mathrm{0}.\mathrm{01}^{\mathrm{o}} \right)\left(\mathrm{1}+\mathrm{tan}\:\mathrm{0}.\mathrm{02}^{\mathrm{o}} \right) \\ $$$$\left(\mathrm{1}+\mathrm{tan}\:\mathrm{0}.\mathrm{03}^{\mathrm{o}} \right)...\left(\mathrm{1}+\mathrm{tan}\:\mathrm{44}.\mathrm{99}^{\mathrm{o}} \right) \\ $$

Question Number 79763    Answers: 1   Comments: 2

calculate ∫_0 ^π {cos^8 x +sin^8 x}dx

$${calculate}\:\int_{\mathrm{0}} ^{\pi} \left\{{cos}^{\mathrm{8}} {x}\:+{sin}^{\mathrm{8}} {x}\right\}{dx} \\ $$

Question Number 79761    Answers: 1   Comments: 1

(x^2 +2)y′′ + xy = 0

$$\left({x}^{\mathrm{2}} +\mathrm{2}\right){y}''\:+\:{xy}\:=\:\mathrm{0} \\ $$

Question Number 79758    Answers: 0   Comments: 1

find value of ∫_0 ^1 ln(1+ix^2 )dx and ∫_0 ^1 ln(1−ix^2 )dx with i=(√(−1))

$${find}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{ix}^{\mathrm{2}} \right){dx}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{ix}^{\mathrm{2}} \right){dx}\:{with}\:{i}=\sqrt{−\mathrm{1}} \\ $$

Question Number 79757    Answers: 0   Comments: 1

And equation of a circle is x^2 +y^2 −2x+4y=0. (T) is his his tangent line at M(x_0 ;y_0 ) passing by D(2;1). a) Show that y verify y_0 ^2 +y_0 =0 b) deduct others tangent′s equations to Circle passing by D.

$$\mathrm{And}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{is} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{4}{y}=\mathrm{0}. \\ $$$$\left({T}\right)\:\mathrm{is}\:\mathrm{his}\:\mathrm{his}\:\mathrm{tangent}\:\mathrm{line}\:\mathrm{at}\:\mathrm{M}\left({x}_{\mathrm{0}} ;{y}_{\mathrm{0}} \right) \\ $$$${passing}\:{by}\:{D}\left(\mathrm{2};\mathrm{1}\right). \\ $$$$ \\ $$$$\left.\mathrm{a}\right)\:\mathrm{Show}\:\mathrm{that}\:\mathrm{y}\:\mathrm{verify}\:\mathrm{y}_{\mathrm{0}} ^{\mathrm{2}} +\mathrm{y}_{\mathrm{0}} =\mathrm{0} \\ $$$$\left.\mathrm{b}\right)\:\mathrm{deduct}\:\mathrm{others}\:\mathrm{tangent}'\mathrm{s}\: \\ $$$$\mathrm{equations}\:\mathrm{to}\:\mathrm{Circle}\:\mathrm{passing}\:\mathrm{by}\:\mathrm{D}. \\ $$

Question Number 79751    Answers: 2   Comments: 0

prove that cos^6 θ + sin^6 θ = 1 − (3/4) sin^2 2θ

$${prove}\:{that}\:\mathrm{cos}\:^{\mathrm{6}} \theta\:+\:\mathrm{sin}\:^{\mathrm{6}} \theta\:=\:\mathrm{1}\:−\:\frac{\mathrm{3}}{\mathrm{4}}\:\mathrm{sin}\:^{\mathrm{2}} \mathrm{2}\theta \\ $$

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