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Question Number 82815 Answers: 0 Comments: 2

lim_(x→0^+ ) (1/((1+(1/x))^(1/(ln(x))) ))=?

$$\underset{{x}\rightarrow\mathrm{0}^{+} } {{lim}}\:\frac{\mathrm{1}}{\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{\frac{\mathrm{1}}{{ln}\left({x}\right)}} }=? \\ $$

Question Number 82759 Answers: 1 Comments: 0

find the value of (√(2+(√(2+(√(2+(√(2cos 80^o )))))))) =

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2cos}\:\mathrm{80}^{{o}} }}}}\:=\: \\ $$

Question Number 82755 Answers: 1 Comments: 2

calculate ∫_0 ^∞ ((lnx)/((1+x^2 )^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{lnx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx} \\ $$

Question Number 82753 Answers: 0 Comments: 3

Question Number 82761 Answers: 0 Comments: 7

lim_(x→0) (((cosx)^(1/m) −(cosx)^(1/n) )/x^2 ) [where m and n integer]

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left({cosx}\right)^{\frac{\mathrm{1}}{{m}}} −\left({cosx}\right)^{\frac{\mathrm{1}}{{n}}} }{{x}^{\mathrm{2}} }\:\:\left[{where}\:{m}\:{and}\:{n}\:{integer}\right] \\ $$

Question Number 82768 Answers: 0 Comments: 1

Question Number 82767 Answers: 1 Comments: 1

If ((sin (A+θ))/(sin (B+θ))) = (√((sin 2A)/(sin 2B))) prove that tan^2 θ = tan A.tan B

$$\mathrm{If}\:\frac{\mathrm{sin}\:\left(\mathrm{A}+\theta\right)}{\mathrm{sin}\:\left({B}+\theta\right)}\:=\:\sqrt{\frac{\mathrm{sin}\:\mathrm{2}{A}}{\mathrm{sin}\:\mathrm{2}{B}}} \\ $$$${prove}\:{that}\:\mathrm{tan}\:^{\mathrm{2}} \theta\:=\:\mathrm{tan}\:{A}.\mathrm{tan}\:{B} \\ $$

Question Number 82729 Answers: 1 Comments: 2

Question Number 82726 Answers: 0 Comments: 10

Question Number 82721 Answers: 1 Comments: 2

show that ∫xe^(−x^6 ) sin(x^3 ) dx=((Γ((5/6)))/3) 1F1[(5/6);(3/2);((−1)/4)]

$${show}\:{that}\: \\ $$$$\int{xe}^{−{x}^{\mathrm{6}} } \:{sin}\left({x}^{\mathrm{3}} \right)\:{dx}=\frac{\Gamma\left(\frac{\mathrm{5}}{\mathrm{6}}\right)}{\mathrm{3}}\:\mathrm{1}{F}\mathrm{1}\left[\frac{\mathrm{5}}{\mathrm{6}};\frac{\mathrm{3}}{\mathrm{2}};\frac{−\mathrm{1}}{\mathrm{4}}\right] \\ $$

Question Number 82719 Answers: 2 Comments: 3

If x,y ∈R satisfy in equation x−4(√y) = 2(√(x−y)) . find range of x

$$\mathrm{If}\:\mathrm{x},{y}\:\in\mathbb{R}\:{satisfy}\:{in}\:{equation}\: \\ $$$${x}−\mathrm{4}\sqrt{{y}}\:=\:\mathrm{2}\sqrt{{x}−{y}}\:.\:{find}\:{range}\:{of}\:{x} \\ $$

Question Number 82701 Answers: 1 Comments: 0

2f(x−1) +3f(x+1) ^ = 3x^2 −5x find f(x)

$$\mathrm{2}{f}\left({x}−\mathrm{1}\right)\:+\mathrm{3}{f}\left({x}+\mathrm{1}\right)\overset{\:} {\:}=\:\mathrm{3}{x}^{\mathrm{2}} −\mathrm{5}{x} \\ $$$${find}\:{f}\left({x}\right) \\ $$

Question Number 82700 Answers: 1 Comments: 4

∫ ((2dx)/(3x(√(5x^2 +6)))) ?

$$\int\:\frac{\mathrm{2}{dx}}{\mathrm{3}{x}\sqrt{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{6}}}\:? \\ $$

Question Number 82699 Answers: 0 Comments: 3

lim_(x→1) (((√(ax−a+b))−3)/(x−1)) = −(3/2) find a and b without L′hopital rule

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt{{ax}−{a}+{b}}−\mathrm{3}}{{x}−\mathrm{1}}\:=\:−\frac{\mathrm{3}}{\mathrm{2}} \\ $$$${find}\:{a}\:{and}\:{b}\:{without}\:{L}'{hopital}\:{rule} \\ $$

Question Number 82687 Answers: 0 Comments: 5

Question Number 82682 Answers: 0 Comments: 3

Help me please....!! Lim_(x→0) ((1/(ex)))^(6x) =...

$$\mathrm{Help}\:\mathrm{me}\:\mathrm{please}....!! \\ $$$$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{Lim}}\:\left(\frac{\mathrm{1}}{\mathrm{ex}}\right)^{\mathrm{6x}} =... \\ $$

Question Number 82667 Answers: 1 Comments: 0

if a>0 b>0 a≤b show that a^2 ≤(((2ab)/(a+b)))^2 ≤ab≤(((a+b)/2))^2 ≤((a^2 +b^2 )/2)≤b^2

$${if}\:{a}>\mathrm{0}\:\:{b}>\mathrm{0}\:\:{a}\leqslant{b} \\ $$$$ \\ $$$${show}\:{that}\: \\ $$$${a}^{\mathrm{2}} \leqslant\left(\frac{\mathrm{2}{ab}}{{a}+{b}}\right)^{\mathrm{2}} \leqslant{ab}\leqslant\left(\frac{{a}+{b}}{\mathrm{2}}\right)^{\mathrm{2}} \leqslant\frac{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }{\mathrm{2}}\leqslant{b}^{\mathrm{2}} \\ $$

Question Number 82665 Answers: 1 Comments: 2

(√(6561(√(6561(√(6561(√(6561(√(...)))))))))) = 3^( 8^x ) (√(6561(√(...)))) (60 time) find x

$$\sqrt{\mathrm{6561}\sqrt{\mathrm{6561}\sqrt{\mathrm{6561}\sqrt{\mathrm{6561}\sqrt{...}}}}}\:=\:\mathrm{3}^{\:\mathrm{8}^{{x}} \:} \\ $$$$\sqrt{\mathrm{6561}\sqrt{...}}\:\:\left(\mathrm{60}\:{time}\right) \\ $$$${find}\:{x} \\ $$

Question Number 82654 Answers: 3 Comments: 1

If sec x + tan x = 2+(√5) find sin x+ cos x ?

$$\boldsymbol{\mathrm{I}}\mathrm{f}\:\mathrm{sec}\:\mathrm{x}\:+\:\mathrm{tan}\:\mathrm{x}\:=\:\mathrm{2}+\sqrt{\mathrm{5}} \\ $$$$\mathrm{find}\:\mathrm{sin}\:\mathrm{x}+\:\mathrm{cos}\:\mathrm{x}\:? \\ $$

Question Number 82647 Answers: 0 Comments: 2

In the rectangular region, −2<x<2, −3<y<3, the surface charge density is given as ρ_s =(x^2 +y^2 +1)^(3/2) . If no other charge is present, find E at P(0,0,1).

$${In}\:{the}\:{rectangular}\:{region},\:−\mathrm{2}<{x}<\mathrm{2}, \\ $$$$−\mathrm{3}<{y}<\mathrm{3},\:{the}\:{surface}\:{charge}\:{density} \\ $$$${is}\:{given}\:{as}\:\rho_{{s}} =\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} .\:{If}\:{no}\:{other} \\ $$$${charge}\:{is}\:{present},\:{find}\:{E}\:{at}\:{P}\left(\mathrm{0},\mathrm{0},\mathrm{1}\right). \\ $$

Question Number 82644 Answers: 1 Comments: 2

Question Number 82638 Answers: 0 Comments: 4

given x= cos^3 x what is x ?

$${given}\:{x}=\:\mathrm{cos}\:^{\mathrm{3}} {x} \\ $$$${what}\:{is}\:{x}\:? \\ $$

Question Number 82631 Answers: 0 Comments: 1

Eight point charges of 1nC each are located at corners of the cube in free space that is 1m on a side . Find ∣E∣ at the centre of an edge. (Assume origin to be centre of cube).

$${Eight}\:{point}\:{charges}\:{of}\:\mathrm{1}{nC}\:{each}\:{are} \\ $$$${located}\:{at}\:{corners}\:{of}\:{the}\:{cube}\:{in}\:{free} \\ $$$${space}\:{that}\:{is}\:\mathrm{1}{m}\:{on}\:{a}\:{side}\:.\:{Find}\:\:\mid\boldsymbol{{E}}\mid \\ $$$${at}\:{the}\:{centre}\:{of}\:{an}\:{edge}. \\ $$$$\left({Assume}\:{origin}\:{to}\:{be}\:{centre}\:{of}\:{cube}\right). \\ $$

Question Number 82628 Answers: 1 Comments: 1

If a,b, c are in Harmonic progression find the value of ((a+b)/(b−a)) + ((b+c)/(b−c)) . ?

$${If}\:{a},{b},\:{c}\:{are}\:{in}\:{Harmonic}\:{progression} \\ $$$${find}\:{the}\:{value}\:{of}\:\frac{{a}+{b}}{{b}−{a}}\:+\:\frac{{b}+{c}}{{b}−{c}}\:.\:? \\ $$

Question Number 82627 Answers: 0 Comments: 1

A 20nC point charge is located at P(2,4,−3) in free space. Find the locus of all points at which E_r =1V/m.

$${A}\:\mathrm{20}{nC}\:{point}\:{charge}\:{is}\:{located}\:{at} \\ $$$${P}\left(\mathrm{2},\mathrm{4},−\mathrm{3}\right)\:{in}\:{free}\:{space}.\:\boldsymbol{{F}}{ind}\:{the}\:{locus} \\ $$$${of}\:{all}\:{points}\:{at}\:{which}\:{E}_{{r}} =\mathrm{1}{V}/{m}. \\ $$

Question Number 82639 Answers: 0 Comments: 3

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