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Question Number 210079    Answers: 0   Comments: 0

Find directional derivatives(D_v )of f(x,y,z)=3xy^3 −2xz^2 in the direction of the v=2i−3j+6k. then Evaluate directional derivatives at the point (3,1,−2)

$${Find}\:{directional}\:{derivatives}\left({D}_{{v}} \right){of}\:\: \\ $$$${f}\left({x},{y},{z}\right)=\mathrm{3}{xy}^{\mathrm{3}} −\mathrm{2}{xz}^{\mathrm{2}} \:\:{in}\:{the}\:{direction}\:{of}\:{the} \\ $$$${v}=\mathrm{2}{i}−\mathrm{3}{j}+\mathrm{6}{k}. \\ $$$${then}\:{Evaluate}\:{directional}\:{derivatives}\: \\ $$$${at}\:{the}\:{point}\:\left(\mathrm{3},\mathrm{1},−\mathrm{2}\right) \\ $$

Question Number 210078    Answers: 1   Comments: 0

Find the directional derivative of f(x,y)=4x^3 −3x^2 y^2 in the direction given by the angle θ=(π/3) and also Evaluate directional derivatives at the point (1,2)

$${Find}\:{the}\:{directional}\:{derivative}\:{of} \\ $$$${f}\left({x},{y}\right)=\mathrm{4}{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} {y}^{\mathrm{2}} \:\:\:{in}\:{the}\:{direction}\:{given} \\ $$$${by}\:{the}\:{angle}\:\theta=\frac{\pi}{\mathrm{3}}\: \\ $$$${and}\:{also}\:{Evaluate}\:{directional}\:{derivatives} \\ $$$${at}\:{the}\:{point}\:\left(\mathrm{1},\mathrm{2}\right) \\ $$

Question Number 210072    Answers: 2   Comments: 0

Question Number 210060    Answers: 1   Comments: 0

∫_0 ^(+∞) (n/(sin^2 n+nx^2 ))dx

$$\int_{\mathrm{0}} ^{+\infty} \frac{{n}}{{sin}^{\mathrm{2}} {n}+{nx}^{\mathrm{2}} }{dx} \\ $$$$ \\ $$

Question Number 210122    Answers: 1   Comments: 1

Question Number 210050    Answers: 3   Comments: 0

Question Number 210044    Answers: 1   Comments: 3

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

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

Question Number 210036    Answers: 4   Comments: 0

Question Number 210034    Answers: 1   Comments: 4

Question Number 210032    Answers: 3   Comments: 0

∫_6 ^0 (2+5x)e^((1/3)x) dx

$$\int_{\mathrm{6}} ^{\mathrm{0}} \left(\mathrm{2}+\mathrm{5}\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{e}}^{\frac{\mathrm{1}}{\mathrm{3}}\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{dx}} \\ $$

Question Number 210031    Answers: 0   Comments: 0

∫_0 ^(π/2) ((1−xcot(x))/x^2 )dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}−\boldsymbol{\mathrm{xcot}}\left(\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\boldsymbol{\mathrm{dx}} \\ $$

Question Number 210025    Answers: 0   Comments: 1

Question Number 210017    Answers: 0   Comments: 0

MATH−WHIZZKID using kamke find the genral solution for the differential equation 1. x^2 y′′+x^2 y′−2y=0 −−−−−−−−− solve this using forbenius mtd 1.x^2 y′′+(x^3 −3x)y′+(4−2x)y=0 −−−−−−−− solve the differential eqn by power series 1. y′′−2xy′+2py=0 −−−−−−−−− use perseval′s theorem to ∫_0 ^∞ ((cos^2 (𝛂(𝛑/2)))/((1−𝛂^2 )^2 ))dx. −−−−−−−−−− evaluate this integral by contour integration 1. ∫_0 ^∞ ((cos^2 (𝛂(𝛑/2)))/((1−𝛂^2 )^2 ))dx. −−−−−−−−− ∮_c ((1+e^(i𝛑z) )/((z−1)^2 (z+1)^2 ))dz c−upper half plane klipto−quanta⊎

$$ \\ $$$$\boldsymbol{\mathrm{MATH}}−\boldsymbol{\mathrm{WHIZZKID}} \\ $$$$\boldsymbol{\mathrm{using}}\:\boldsymbol{\mathrm{kamke}}\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{genral}} \\ $$$$\boldsymbol{\mathrm{solution}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equation}} \\ $$$$\mathrm{1}.\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}''+\boldsymbol{\mathrm{x}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}'−\mathrm{2}\boldsymbol{\mathrm{y}}=\mathrm{0} \\ $$$$−−−−−−−−− \\ $$$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{using}}\:\boldsymbol{\mathrm{forbenius}}\:\boldsymbol{\mathrm{mtd}} \\ $$$$\mathrm{1}.\boldsymbol{\mathrm{x}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}''+\left(\boldsymbol{\mathrm{x}}^{\mathrm{3}} −\mathrm{3}\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{y}}'+\left(\mathrm{4}−\mathrm{2}\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{y}}=\mathrm{0} \\ $$$$−−−−−−−− \\ $$$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{eqn}}\:\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{power}}\:\boldsymbol{\mathrm{series}} \\ $$$$\mathrm{1}.\:\boldsymbol{\mathrm{y}}''−\mathrm{2}\boldsymbol{\mathrm{xy}}'+\mathrm{2}\boldsymbol{\mathrm{py}}=\mathrm{0} \\ $$$$−−−−−−−−− \\ $$$$\boldsymbol{\mathrm{use}}\:\boldsymbol{\mathrm{perseval}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{theorem}}\:\boldsymbol{\mathrm{to}} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \left(\boldsymbol{\alpha}\frac{\boldsymbol{\pi}}{\mathrm{2}}\right)}{\left(\mathrm{1}−\boldsymbol{\alpha}^{\mathrm{2}} \right)^{\mathrm{2}} }\boldsymbol{\mathrm{dx}}. \\ $$$$−−−−−−−−−− \\ $$$$\boldsymbol{\mathrm{evaluate}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{integral}}\:\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{contour}}\:\boldsymbol{\mathrm{integration}} \\ $$$$\mathrm{1}.\:\int_{\mathrm{0}} ^{\infty} \frac{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \left(\boldsymbol{\alpha}\frac{\boldsymbol{\pi}}{\mathrm{2}}\right)}{\left(\mathrm{1}−\boldsymbol{\alpha}^{\mathrm{2}} \right)^{\mathrm{2}} }\boldsymbol{\mathrm{dx}}. \\ $$$$−−−−−−−−− \\ $$$$\oint_{\boldsymbol{\mathrm{c}}} \frac{\mathrm{1}+\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{i}\pi\mathrm{z}}} }{\left(\boldsymbol{\mathrm{z}}−\mathrm{1}\right)^{\mathrm{2}} \left(\boldsymbol{\mathrm{z}}+\mathrm{1}\right)^{\mathrm{2}} }\boldsymbol{\mathrm{dz}} \\ $$$$\boldsymbol{\mathrm{c}}−\mathrm{upper}\:\mathrm{half}\:\mathrm{plane} \\ $$$$\boldsymbol{\mathrm{klipto}}−\boldsymbol{\mathrm{quanta}}\biguplus \\ $$

Question Number 210014    Answers: 2   Comments: 3

Question Number 210013    Answers: 1   Comments: 0

If f(x)= x^2 +ax+b. if f(1)= 3 and and one of the roots of the eqiation f(x)= 0 doubles the other, find the positive values of a and b.

$$\:{If}\:{f}\left({x}\right)=\:{x}^{\mathrm{2}} +{ax}+{b}.\:{if}\:{f}\left(\mathrm{1}\right)=\:\mathrm{3}\:{and}\: \\ $$$$\:{and}\:{one}\:{of}\:{the}\:{roots}\:{of}\:{the}\:{eqiation} \\ $$$$\:{f}\left({x}\right)=\:\mathrm{0}\:{doubles}\:{the}\:{other},\:{find}\:{the} \\ $$$$\:{positive}\:{values}\:{of}\:{a}\:{and}\:{b}. \\ $$

Question Number 210011    Answers: 0   Comments: 0

Find: ∫_0 ^( 1) ((ln (cos (((πx)/2))))/(x^2 + x)) dx = ?

$$\mathrm{Find}:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\:\frac{\mathrm{ln}\:\left(\mathrm{cos}\:\left(\frac{\pi\mathrm{x}}{\mathrm{2}}\right)\right)}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}}\:\mathrm{dx}\:\:=\:\:? \\ $$

Question Number 209999    Answers: 3   Comments: 0

lim_(x→0) ((e^x −1)/( (√(1−cosx)))) =?

$$\:\:\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{lim}}}\:\frac{\boldsymbol{{e}}^{\boldsymbol{{x}}} −\mathrm{1}}{\:\sqrt{\mathrm{1}−\boldsymbol{{cosx}}}}\:=? \\ $$

Question Number 209991    Answers: 2   Comments: 0

((10^(log _3 (6)) . 15^(log _3 ((2/3))) )/(6^(log _3 ((2/3))) . 5^(log _3 ((4/3))) )) =?

$$\:\:\:\:\:\frac{\mathrm{10}^{\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{6}\right)} .\:\mathrm{15}^{\mathrm{log}\:_{\mathrm{3}} \left(\frac{\mathrm{2}}{\mathrm{3}}\right)} }{\mathrm{6}^{\mathrm{log}\:_{\mathrm{3}} \left(\frac{\mathrm{2}}{\mathrm{3}}\right)} .\:\mathrm{5}^{\mathrm{log}\:_{\mathrm{3}} \left(\frac{\mathrm{4}}{\mathrm{3}}\right)} }\:=?\: \\ $$

Question Number 209988    Answers: 0   Comments: 0

Question Number 209986    Answers: 1   Comments: 0

Solve ax^3 −bx(√x) +c=0 (a, b, c)∈R^3 and x∈R (the value of x for a=1, b=9,c=8)

$$\mathrm{Solve}\: \\ $$$$\:\boldsymbol{\mathrm{ax}}^{\mathrm{3}} −\boldsymbol{\mathrm{bx}}\sqrt{\boldsymbol{\mathrm{x}}}\:+\boldsymbol{\mathrm{c}}=\mathrm{0}\:\:\:\:\: \\ $$$$\:\left(\boldsymbol{\mathrm{a}},\:\boldsymbol{\mathrm{b}},\:\boldsymbol{\mathrm{c}}\right)\in\mathbb{R}^{\mathrm{3}} \:\:\:\:\mathrm{and}\:\boldsymbol{\mathrm{x}}\in\mathbb{R} \\ $$$$\left(\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\boldsymbol{{x}}\:\boldsymbol{{for}}\:\boldsymbol{{a}}=\mathrm{1},\:\:\boldsymbol{{b}}=\mathrm{9},\boldsymbol{{c}}=\mathrm{8}\right) \\ $$

Question Number 209980    Answers: 0   Comments: 7

determiner h ? CD=20 AB=30 h1=25

$$\mathrm{determiner}\:\mathrm{h}\:? \\ $$$$\boldsymbol{\mathrm{CD}}=\mathrm{20}\:\:\:\:\boldsymbol{\mathrm{AB}}=\mathrm{30} \\ $$$$\boldsymbol{\mathrm{h}}\mathrm{1}=\mathrm{25} \\ $$$$ \\ $$

Question Number 209976    Answers: 0   Comments: 1

Question Number 209975    Answers: 1   Comments: 0

Question Number 209974    Answers: 0   Comments: 0

Question Number 209972    Answers: 1   Comments: 0

Question Number 209965    Answers: 1   Comments: 0

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