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what is the value of

eraised to infinity ?if y= x

^{x }+ (sinx)^{x }then find dy/dxplzz help

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

K, x = pi/4 is continuous at x = pi/4

If x

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

^{2 }^{x }+ sin^{-1 }root (3x) with respect to xFIND VALUES OF a , b

If x = sint and y = sinpt prove that :

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

if sqrt(1-x

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

^{2}+1)]^{2 }show that (1+x^{2}) d^{2}y/dx^{2}+xdy/dx =2if x

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

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

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

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

^{2) }where the tangent to the curve has the greatest slopek.c.sinha exercise-13.1 question-

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

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}=0find 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

^{2}y/dx^{2})_{theta= pai/2}The answer: -3/2

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)cot

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

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

If y

^{3 }= 3ax^{2 }- x^{3}then prove that d^{2}y/dx^{2}= -2a^{2}y^{2}/y^{5}if e

^{x}+e^{y}=e^{x+y},prove that dy/dx= -e^{y-x}^{-1}[(a+bcosx)/(b+acosx)] w.r.t xintegration of root tanx ?

tan

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

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

_{If y=cos inverse (sinx+cosx/ root 2) where - pi/4<x<pi/4, then find dy/dx.}^{3}f(x)={(1-cos4x)/x^2 if x k if x=0

(√x)/√16+root of x-4 }

f(x)={ √5x+2 - √4x+4/ x-2.

x (not equal) 2

k. x =2 }

differentiate wrtx

under root (1+sinx/1-sinx)

differentiate w.r.t.x log

_{7}(log_{7}x)types of partial fraction

find the value of K , if the function

f(x) = 1-sinx / (pi-2x)

^{2}, x= pi /23k- 1 , x=pi/2 is continuous at x= pi /2

tan

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

^{2}+ 2 / 1 + 4x^{2})Examine continuity of function f(x) = e

^{1/x}-1 / e^{1/x}+1 at x=0If x = a (θ - sin θ) and y = a (1 - cos θ), find y

_{2}at θ = .^{-1}y = 2log(x+1) show that (x+1)^{2}y + (x+1)y +4y = 0^{2}y/dx^{2}at theta =pai/4 is 4/a .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) .

If y = sin (sin x), prove that

d

^{2}y/dx^{2}+ (tan x) dy/dx + y cos^{2}x = 0.^{( sin x ) ^ ( sin x ) …… infinity}, prove that dy/dx = y^{2}cot x / ( 1 – y log sin x )Y

^{1/m}+ Y^{-1/m}= 2XShow That : (X

^{2}-1)Y_{2}+XY_{1}– m^{2}Y =0_{x6 + root 1-y}^{6 = }^{a3(x3-y3). }prove dy/dx = x^{2}/y^{2}*wholeroot 1-y^{6}/1-x^{6}{ ax+b ≤ c differentiable ?

If x

^{p}y^{q}=(x+y)^{p+q}, then prove that dy/dx=y/x.^{2}-4a^{2})^{1/2}(x^{2}-a^{2}) then dy/dx is^{x}-5^{x}-2^{x}+1/x^{2}when x tends to 0.if

xy_{+}_{y}x =_{a}b find dy/dxIf x=tan(1/a logy) Show that (1+x

^{2})d^{2}y/dx^{2}+ (2x-a)dy/dx = 0sin inverse(a+bcosx/b+acosx)

if x=a sin2t(1+cos2t) and y=b cos2t(1-cos2t) find dy/dx.

(2tanx/tanx +cosx)^2

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

^{2}y/dx^{2.plzzz help}Q:differentiate - tan^-1 (2^[x+1] / 1 - 4^x)

^{y/x}=x, prove that x^{3}d^{2}y/dx^{2 }= (x.dy/dx - y)^{2}^{x/x-y }= a ,prove that ydy/dx + x = 2yPlease 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.^{2}( x not equal to zero) and k ( x = 0 ). find value of k if f(x) is continuous at x=0^{2})y_{2}-xy_{1}-a^{2}y = 0find derivative of y = log {tan(pie/4 + x/2)}

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

y=log( cosec

^{x) }find dy/dxFind d2y/dx2