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what is the value of

eraised to infinity ?If x= 3sint-sin3t, y= 3cost-cos3t, find d^2y/dx^2 at t=pi/3

Find the sum: 7+77+777+.....upto n terms.

^{-1}(cos x / 1+sinx)If x

^{y }=e^{x-y }show thatdy/dx=(logx)/{log(xe)}

^{2 }FIND VALUES OF a , b

If x = sint and y = sinpt prove that :

(1 - xsquare)d2y/dx2 - xdy/dx + psquarey = 0

Q:differentiate - tan^-1 (2^[x+1] / 1 - 4^x)

if sqrt(1-x

^{2)}+ sqrt(1-y^{2}) = a (x-y) prove dy/dx=sqrt((1-y^{2})/(1-x^{2}))if x

^{m}y^{n}= (x+y)^{m+n}show that dy/dx= y/x and find d^{2}y/dx^{2}plzzz help !!

^{-1}[(a+bcosx)/(b+acosx)] w.r.t xif y= [log(x+root x

^{2}+1)]^{2 }show that (1+x^{2}) d^{2}y/dx^{2}+xdy/dx =2if y= sin inverse [ 5x +12 root 1-x2 by 13 find dy by dx

If y = e

^{x}.tan^{-1}x,prove that (1+x^{2})y_{2}2(1-x+x^{2})y_{1}+ (1-x^{2})y = 0^{2) }where the tangent to the curve has the greatest slopedifferentiate wrtx

1)log(a+ bsinx)/(a-bsinx)

2)log

_{7}(log_{7}x)3)(e

^{x}+e^{-x})/(e^{x}-e^{-x})k.c.sinha exercise-13.1 question-

y=xlog(x/(a+bx)), prove that x^3Xd^2y/dx^2 = (x(dy/dx)-y)^2

y= (x + 1/x )

^{x}+ (x^{1+1/x})Differentiate tan

^{-1}[ (root 1 - x^{2}) / x ]^{}w.r.t. cos^{-1}[2x (root 1 - x^{2})].if e

^{x}+e^{y}=e^{x+y},prove that dy/dx+e^{y-x}=0cot

^{-1}( 1 + x / 1 - x )The answer : -1 / 1 + x

^{2}find the value of 'a' for which the function f defined by

f(x)={a sin( pie/2) x+1 ,x

<0{(tan x -sinx) / x

^{3},x>0is continuous at x=0

^{x }/ x^{8}√x +bx^2 - √x / b x^3/2 , x >0

function is continuous at x=0

show that the function f(x)=|x-1|+|x+1|, for all x belongs to R is not differentiable at the point x= -1 and x=1.c ,x=0

(under root x+bx)-(under root x)/b under root x

^{3}, x>0 is constant at x=0^{}if Cosy= xCos(a+y), show that dy/dx= cos

^{2}(a+y)/sin(a)K, x = pi/4 is continuous at x = pi/4

show that f(x) =|x-2| is continuous but not differentiable at x=2. Please reply!!URGENT!!!

{ ax+b ≤ c differentiable ?

prove that

dy/dx= 2 - x/y

if e

^{x}+e^{y}=e^{x+y},prove that dy/dx= -e^{y-x}_{If y=cos inverse (sinx+cosx/ root 2) where - pi/4<x<pi/4, then find dy/dx.}integration of root tanx ?

differentiate w.r.t.x log

_{7}(log_{7}x)if siny= xsin(a+y),then prove that dy/dx=sin^2(a+y)/sin a

^{x/x-y }= a ,prove that ydy/dx + x = 2y^{3}+4, t= x^{2 }+ 2xf(x)={(1-cos4x)/x^2 if x k if x=0

(√x)/√16+root of x-4 }

differentiate wrtx

under root (1+sinx/1-sinx)

If f(x) = {(3+x)/(1+x)}

^{2+3x}, find f '(0).types of partial fraction

Find dy/dx , when y = (sin x + x

^{2}) /^{}(cot 2x) .tan

^{-1}( 5x / 1 - 6x^{2})The answer:( 3 / 1 + 9x

^{2}+ 2 / 1 + 4x^{2})if y=cos

^{-1}(3+5cosx)/(5+3cosx) find dy/dx?????If x = a (θ - sin θ) and y = a (1 - cos θ), find y

_{2}at θ = .4. Find the value of k, for Which the function

$f\left(x\right)=\left\{\begin{array}{l}\frac{\sqrt{1+kx}-\sqrt{1-kx}}{x},if-1\le x0\\ \frac{2x+1}{x-1},if0\le x1\end{array}\right.$is continuous at x=O.

find the derivative of cos root x wrt x from first principle??

Find the intervals in which the function f(x) = sin^4x + cos^4x is increasing or decreasing where the range of x is ( 0, pie/2) .

^{2}and y = 3 + 2 log t / t , show that dy/dx = tIf y = sin (sin x), prove that

d

^{2}y/dx^{2}+ (tan x) dy/dx + y cos^{2}x = 0.f(x)={ √5x+2 - √4x+4/ x-2.

x (not equal) 2

k. x =2 }

_{x6 + root 1-y}^{6 = }^{a3(x3-y3). }prove dy/dx = x^{2}/y^{2}*wholeroot 1-y^{6}/1-x^{6}if y=x^e^-x^2,find dy/dx

If x

^{p}y^{q}=(x+y)^{p+q}, then prove that dy/dx=y/x.Differentiate

y=log( cosec

^{x) }find dy/dxExamine continuity of function f(x) = e

^{1/x}-1 / e^{1/x}+1 at x=0x

^{2}/ a^{2}+ y^{2}/ b^{2}= 1The answer: - b

^{2}x / a^{2}yif

xy_{+}_{y}x =_{a}b find dy/dxDifferentiate w.r.t. x : y = tan

^{-1}[ (under root 1 + a^{2}x^{2}) - 1 / ax ]If x=tan(1/a logy) Show that (1+x

^{2})d^{2}y/dx^{2}+ (2x-a)dy/dx = 0if x=a sin2t(1+cos2t) and y=b cos2t(1-cos2t) find dy/dx.

^{3}+ x^{2}- 16x +20/ (x-2)^{2}, x is not equal 2k , x=2

find k if f(x) is continuous for all x

if x=2cost -cos2t and y=2sint -sin2t . find d

^{2}y/dx^{2.plzzz help}$\mathbf{4}\mathbf{.}\underset{h\to 0}{\mathrm{lim}}\frac{\mathrm{tan}\left(a+2h\right)-2\mathrm{tan}\left(a+h\right)+\mathrm{tan}a}{{h}^{2}}isequalto\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(A\right)\mathrm{tan}a\left(B\right){\mathrm{tan}}^{2}a\left(C\right)seca\left(D\right)2\left(se{c}^{2}a\right)\left(\mathrm{tan}a\right)$

^{y/x}=x, prove that x^{3}d^{2}y/dx^{2 }= (x.dy/dx - y)^{2}(2tanx/tanx +cosx)^2

Please solve the following problems.

1. Y = Sin(mSin

^{-1}x) prove that1-x^{2}^{ }- xy^{-1}+m^{2}y = 02

2. Y = Cosec x + Cot x prove that sin x (

d) = y^{2}y^{2}dx

^{2}3. If Y = 3cos(log x) + 4sin(log x) show that x

^{2 }(d) + (^{2}ydy) + y = 0dx

^{2}dxIf log(x

^{2}+y^{2})=2tan^{-1(}y/x), then show that dy/dx=x+y/x-y.^{x})/(1-e^{x}))^{1/2}. Show that dy/dx = e^{x}/((1-e^{x})(1-e^{2x})^{1/2})^{4}, u = 1/v , v = 5x^{2}+2x+6find derivative of y = log {tan(pie/4 + x/2)}

if y=e^x + log x/sin 3x, find dy/dx

^{-1}( x^{2}- y^{2}/ x^{2}+ y^{2}) = tan^{-1}a, prove that dy/dx = y/xIf y

^{3 }= 3ax^{2 }- x^{3}then prove that d^{2}y/dx^{2}= -2a^{2}y^{2}/y^{5}Find d2y/dx2

Please provide a solution of this questio as Ihave stuck to eliminate e

^{x}if y=e

^{x}.tan^{-1}x then prove that (1+x^{2})d^{2}y/dx^{2}-2(1-x+x^{2})dy/dx +(1-x^{2})y=0