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Question Number 84036 Answers: 1 Comments: 0

∫_(−1) ^(10) sin(x−∣x∣) dx

$$\int_{−\mathrm{1}} ^{\mathrm{10}} {sin}\left({x}−\mid{x}\mid\right)\:{dx} \\ $$

Question Number 84035 Answers: 0 Comments: 2

∫((x−4)/(x^4 −1))dx

$$\int\frac{{x}−\mathrm{4}}{{x}^{\mathrm{4}} −\mathrm{1}}{dx} \\ $$

Question Number 84170 Answers: 2 Comments: 0

∫ (dx/(x^3 ((4−x^3 ))^(1/(3 )) )) ?

$$\int\:\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{3}} \:\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{4}−\mathrm{x}^{\mathrm{3}} }}\:?\: \\ $$

Question Number 84030 Answers: 0 Comments: 0

find ∫ (√((x+2)/(x^2 −x−3)))dx

$${find}\:\int\:\sqrt{\frac{{x}+\mathrm{2}}{{x}^{\mathrm{2}} −{x}−\mathrm{3}}}{dx} \\ $$

Question Number 84029 Answers: 0 Comments: 0

let f(x)=e^(−nx) ln(2+x^2 ) with n integr natural 1) calculste f^((n)) (x) and f^((n)) (0) 2) developp f at integr serie 3)find ∫_0 ^1 f(x)d and ∫_0 ^∞ f(x)dx

$${let}\:{f}\left({x}\right)={e}^{−{nx}} {ln}\left(\mathrm{2}+{x}^{\mathrm{2}} \right)\:\:\:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{calculste}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{3}\right){find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{f}\left({x}\right){d}\:{and}\:\int_{\mathrm{0}} ^{\infty} {f}\left({x}\right){dx} \\ $$

Question Number 84021 Answers: 3 Comments: 1

Question Number 84019 Answers: 2 Comments: 2

Show that: 1• tan3x=((3−tan^2 x)/(1−3tan^2 x)) using cos3x=4cos^4 x−3cosx sin3x=−4sin^3 x+3sinx Thanks...

$${Show}\:{that}: \\ $$$$\mathrm{1}\bullet\:\:\:{tan}\mathrm{3}{x}=\frac{\mathrm{3}−{tan}^{\mathrm{2}} {x}}{\mathrm{1}−\mathrm{3}{tan}^{\mathrm{2}} {x}} \\ $$$${using}\:{cos}\mathrm{3}{x}=\mathrm{4}{cos}^{\mathrm{4}} {x}−\mathrm{3}{cosx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{sin}\mathrm{3}{x}=−\mathrm{4}{sin}^{\mathrm{3}} {x}+\mathrm{3}{sinx} \\ $$$${Thanks}... \\ $$

Question Number 84018 Answers: 0 Comments: 0

Question Number 84014 Answers: 0 Comments: 1

find the no. of positivve integral solutions of x+y+2z=89 x>10 y>20 z>2

$${find}\:{the}\:{no}.\:{of}\:{positivve} \\ $$$${integral}\:{solutions}\:{of} \\ $$$${x}+{y}+\mathrm{2}{z}=\mathrm{89} \\ $$$${x}>\mathrm{10} \\ $$$${y}>\mathrm{20} \\ $$$${z}>\mathrm{2} \\ $$

Question Number 84002 Answers: 0 Comments: 0

((sin(x))/(√(2sin^2 (x)+cos^2 (x)))) +(1/(√2))=csc(x)(√(2sin^2 (x)+cos^2 (x))) show that x={(π/2)+2πn} and x={cos^(−1) ((√3))−π+2πn} and x={−cos^(−1) ((√3))+2πn}

$$\frac{{sin}\left({x}\right)}{\sqrt{\mathrm{2}{sin}^{\mathrm{2}} \left({x}\right)+{cos}^{\mathrm{2}} \left({x}\right)}}\:+\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}={csc}\left({x}\right)\sqrt{\mathrm{2}{sin}^{\mathrm{2}} \left({x}\right)+{cos}^{\mathrm{2}} \left({x}\right)} \\ $$$${show}\:{that} \\ $$$${x}=\left\{\frac{\pi}{\mathrm{2}}+\mathrm{2}\pi{n}\right\}\:{and}\:{x}=\left\{{cos}^{−\mathrm{1}} \left(\sqrt{\mathrm{3}}\right)−\pi+\mathrm{2}\pi{n}\right\} \\ $$$${and}\:{x}=\left\{−{cos}^{−\mathrm{1}} \left(\sqrt{\mathrm{3}}\right)+\mathrm{2}\pi{n}\right\} \\ $$$$ \\ $$

Question Number 84001 Answers: 0 Comments: 2

Question Number 84000 Answers: 1 Comments: 1

Question Number 83999 Answers: 0 Comments: 0

Question Number 83991 Answers: 0 Comments: 1

Find the locus of the points represented by the complex number ,z, such that 2∣z−3∣ = ∣z−6i∣

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{the}\:\mathrm{points}\:\mathrm{represented}\:\mathrm{by} \\ $$$$\mathrm{the}\:\mathrm{complex}\:\mathrm{number}\:,{z},\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{2}\mid{z}−\mathrm{3}\mid\:=\:\mid{z}−\mathrm{6i}\mid \\ $$

Question Number 83989 Answers: 0 Comments: 3

find a. ∫cos 3x cos 5x dx b. ∫xln 2x dx

$$\mathrm{find}\:\: \\ $$$$\mathrm{a}.\:\:\:\int\mathrm{cos}\:\mathrm{3}{x}\:\mathrm{cos}\:\mathrm{5}{x}\:{dx} \\ $$$$\mathrm{b}.\:\:\int{x}\mathrm{ln}\:\mathrm{2}{x}\:{dx} \\ $$

Question Number 83984 Answers: 1 Comments: 0

∫cos^7 (x) dx

$$\int{cos}^{\mathrm{7}} \left({x}\right)\:{dx} \\ $$

Question Number 84005 Answers: 2 Comments: 4

find atleast 7 solutions of the equation. 900x+7689y=109876 CAN ANYONE SOLVE THIS now lets find 7 integral solutions

$${find}\:{atleast}\:\mathrm{7}\:{solutions} \\ $$$${of}\:{the}\:{equation}. \\ $$$$\mathrm{900}{x}+\mathrm{7689}{y}=\mathrm{109876} \\ $$$${CAN}\:{ANYONE}\:{SOLVE} \\ $$$${THIS} \\ $$$${now}\:{lets}\:{find}\:\mathrm{7}\:{integral} \\ $$$${solutions} \\ $$

Question Number 84004 Answers: 0 Comments: 0

Question Number 83977 Answers: 2 Comments: 0

find range function f(x)= x(√(7x−x^2 −1)) without calculus

$$\mathrm{find}\:\mathrm{range}\:\mathrm{function}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{x}\sqrt{\mathrm{7x}−\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\:\mathrm{without} \\ $$$$\mathrm{calculus} \\ $$

Question Number 83975 Answers: 2 Comments: 0

find solution 8 tan x−8tan^5 x = sec^6 x in x∈ (0, (π/2))

$$\mathrm{find}\:\mathrm{solution} \\ $$$$\mathrm{8}\:\mathrm{tan}\:\mathrm{x}−\mathrm{8tan}\:^{\mathrm{5}} \mathrm{x}\:=\:\mathrm{sec}\:^{\mathrm{6}} \mathrm{x}\:\mathrm{in}\:\mathrm{x}\in\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\right) \\ $$

Question Number 83966 Answers: 2 Comments: 0

prove that for any complex number z, if ∣z∣ < 1, then Re(z + 1) > 0

$$\mathrm{prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{any}\:\mathrm{complex}\:\mathrm{number}\:{z},\:\mathrm{if}\: \\ $$$$\:\mid{z}\mid\:<\:\mathrm{1},\:\mathrm{then}\:\mathrm{Re}\left({z}\:+\:\mathrm{1}\right)\:>\:\mathrm{0} \\ $$

Question Number 83965 Answers: 0 Comments: 3

prove or disprove(with counter−example) that a) For all two dimensional vectors a,b,c, a.b = a. c ⇒ b=c. b) For all positive real numbers a,b. ((a +b)/2) ≥ (√(ab))

Question Number 83964 Answers: 1 Comments: 0

The graph of y = ((a + bx)/((x−1)(x−4))) has a turning point at P(2,−1). Find the value of a and b and hence,sketch the curve y = f(x) showing clearly the turning points, asympototes and intercept(s) with the axes.

$$\mathrm{The}\:\mathrm{graph}\:\mathrm{of}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}\:=\:\frac{{a}\:+\:{bx}}{\left({x}−\mathrm{1}\right)\left({x}−\mathrm{4}\right)} \\ $$$$\mathrm{has}\:\mathrm{a}\:\mathrm{turning}\:\mathrm{point}\:\mathrm{at}\:{P}\left(\mathrm{2},−\mathrm{1}\right).\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{a}\:\mathrm{and}\:{b}\: \\ $$$$\mathrm{and}\:\mathrm{hence},\mathrm{sketch}\:\mathrm{the}\:\mathrm{curve}\:{y}\:=\:{f}\left({x}\right)\:\mathrm{showing}\:\mathrm{clearly}\:\mathrm{the} \\ $$$$\mathrm{turning}\:\mathrm{points},\:\mathrm{asympototes}\:\mathrm{and}\:\mathrm{intercept}\left(\mathrm{s}\right)\:\mathrm{with}\:\mathrm{the} \\ $$$$\mathrm{axes}. \\ $$

Question Number 83961 Answers: 0 Comments: 1

find I =∫ e^(−x) cos^4 xdx and J =∫ e^(−x) sin^4 xdx

$${find}\:{I}\:=\int\:{e}^{−{x}} \:{cos}^{\mathrm{4}} {xdx}\:\:{and}\:{J}\:=\int\:{e}^{−{x}} \:{sin}^{\mathrm{4}} \:{xdx} \\ $$

Question Number 83960 Answers: 2 Comments: 1

∫ ((x−1)/(√(x^2 −x))) dx ?

$$\int\:\frac{\mathrm{x}−\mathrm{1}}{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}}}\:\mathrm{dx}\:?\: \\ $$

Question Number 83956 Answers: 1 Comments: 1

for x ∈ R satisfy the equation f(x)+3x f((1/x)) = 2(x+1) find f(2019) .

$$\mathrm{for}\:\mathrm{x}\:\in\:\mathbb{R}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{3x}\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:=\:\mathrm{2}\left(\mathrm{x}+\mathrm{1}\right) \\ $$$$\mathrm{find}\:\mathrm{f}\left(\mathrm{2019}\right)\:.\: \\ $$

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