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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.

If x

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

^{2 }FIND VALUES OF a , b

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

If x = sint and y = sinpt prove that :

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

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

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

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

2)log

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

^{x}+e^{-x})/(e^{x}-e^{-x})if x

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

if y= [log(x+root x

^{2}+1)]^{2 }show that (1+x^{2}) d^{2}y/dx^{2}+xdy/dx =2K, x = pi/4 is continuous at x = pi/4

if y= sin inverse [ 5x +12 root 1-x2 by 13 find dy by dx

^{2) }where the tangent to the curve has the greatest slopeIf y = e

^{x}.tan^{-1}x,prove that (1+x^{2})y_{2}2(1-x+x^{2})y_{1}+ (1-x^{2})y = 0k.c.sinha exercise-13.1 question-

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

^{-1}[(a+bcosx)/(b+acosx)] w.r.t xDifferentiate tan

^{-1}[ (root 1 - x^{2}) / x ]^{}w.r.t. cos^{-1}[2x (root 1 - x^{2})].Find dy/dx , when y = (sin x + x

^{2}) /^{}(cot 2x) .if e

^{x}+e^{y}=e^{x+y},prove that dy/dx+e^{y-x}=0^{x/x-y }= a ,prove that ydy/dx + x = 2yx->0

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 +bx^2 - √x / b x^3/2 , x >0

function is continuous at x=0

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){ ax+b ≤ c differentiable ?

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

differentiate w.r.t.x log

_{7}(log_{7}x)f(x)={ √5x+2 - √4x+4/ x-2.

x (not equal) 2

k. x =2 }

if e

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

dy/dx= 2 - x/y

integration of root tanx ?

7. For what value of K, F(X)= {tan3x/sin2x when x not equal to 0

and 2k when x = 0 is continuos for allx belongs to R?

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.y= (x + 1/x )

^{x}+ (x^{1+1/x})if siny= xsin(a+y),then prove that dy/dx=sin^2(a+y)/sin a

^{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

f(x)={(1-cos4x)/x^2 if x k if x=0

(√x)/√16+root of x-4 }

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

differentiate wrtx

under root (1+sinx/1-sinx)

cot

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

^{2}types of partial fraction

If x

^{p}.y^{q}= (x+y)^{p+q }, Prove that(i) dy/dx = y/x

(ii) d

^{2}y/dx^{2}= 0tan

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

^{2}+ 2 / 1 + 4x^{2})If x = a (θ - sin θ) and y = a (1 - cos θ), find y

_{2}at θ = .find the derivative of cos root x wrt x from first principle??

^{2}( x not equal to zero) and k ( x = 0 ). find value of k if f(x) is continuous at x=0Find 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) .

^{x }/ x^{8}If y = sin (sin x), prove that

d

^{2}y/dx^{2}+ (tan x) dy/dx + y cos^{2}x = 0.^{-1}[x*sqrt(1-x) - sqrt(x)*sqrt(1-x^{2})] find dy/dxif y=x^e^-x^2,find dy/dx

_{x6 + root 1-y}^{6 = }^{a3(x3-y3). }prove dy/dx = x^{2}/y^{2}*wholeroot 1-y^{6}/1-x^{6}^{3}If x

^{p}y^{q}=(x+y)^{p+q}, then prove that dy/dx=y/x._{If y=cos inverse (sinx+cosx/ root 2) where - pi/4<x<pi/4, then find dy/dx.}Examine 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/dx^{2}y/dx^{2})_{theta= pai/2}The answer: -3/2

If x=tan(1/a logy) Show that (1+x

^{2})d^{2}y/dx^{2}+ (2x-a)dy/dx = 0^{4}, u = 1/v , v = 5x^{2}+2x+6if x=a sin2t(1+cos2t) and y=b cos2t(1-cos2t) find dy/dx.

^{2}and y = 3 + 2 log t / t , show that dy/dx = tif x=2cost -cos2t and y=2sint -sin2t . find d

^{2}y/dx^{2.plzzz help}Differentiate w.r.t. x : y = tan

^{-1}[ (under root 1 + a^{2}x^{2}) - 1 / ax ]^{y/x}=x, prove that x^{3}d^{2}y/dx^{2 }= (x.dy/dx - y)^{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.sin inverse(a+bcosx/b+acosx)

find derivative of y = log {tan(pie/4 + x/2)}

f(x)={ (1-x

^{n})/(1-x) ; x0,xn-1 ; x=0

check continuity at x=1

^{-1}( x^{2}- y^{2}/ x^{2}+ y^{2}) = tan^{-1}a, prove that dy/dx = y/x^{x})/(1-e^{x}))^{1/2}. Show that dy/dx = e^{x}/((1-e^{x})(1-e^{2x})^{1/2})Find d2y/dx2

X = e

^{theta}( sin theta + cos theta ) , y = e^{theta}( sin theta - cos theta )The answer: tan theta