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Syllabus

what is the value of

eraised to infinity ?^{x}+ 5^{y}= 5^{x+y}prove that dy/dx+ 5^{y-x}= 0Find 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

If x = sint and y = sinpt prove that :

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

^{4}+y^{4}=100, Find the value of dy/dx.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 !!

^{}5^{x}+5^{y}= 5^{x+y }then prove that dy/dx + 5^{y-x}= 0if 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

^{2) }where the tangent to the curve has the greatest slope^{-1}(cos x / 1+sinx)k.c.sinha exercise-13.1 question-

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

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

Differentiate tan

^{-1}[ (root 1 - x^{2}) / x ]^{}w.r.t. cos^{-1}[2x (root 1 - x^{2})].if y=x^e^-x^2,find dy/dx

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

Differentiate

y=log( cosec

^{x) }find dy/dx√x +bx^2 - √x / b x^3/2 , x >0

function is continuous at x=0

then find dy/dx.

Ans : (a+b+c)^(x^(a+b+c-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)Examine the continuity of the function F(x)= 1/ (x-3) for all x belongs to R.

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

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

(2tanx/tanx +cosx)^2

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 ?

For what value of K ,the matrix [2-K 3 ] is not invertible?

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=tan

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

If y

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

types of partial fraction

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?

tan

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

^{2}+ 2 / 1 + 4x^{2})cosec

^{-1}( 1 + x^{2}/ 2x )The answer: 2 / 1 + x

^{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??

For what value of k is the function

f(x)= tan5x sin2x , when x is not equal to zero

k , x=0

continuous at x=0?

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) .

{ ax+b ≤ c differentiable ?

If y = sin (sin x), prove that

d

^{2}y/dx^{2}+ (tan x) dy/dx + y cos^{2}x = 0._{x6 + root 1-y}^{6 = }^{a3(x3-y3). }prove dy/dx = x^{2}/y^{2}*wholeroot 1-y^{6}/1-x^{6}sin

^{-1}{ x^{2}/ root under x^{4}+ a^{4}}The answer: 2a

^{2}x / ( a^{4}+ x^{4})If x

^{p}y^{q}=(x+y)^{p+q}, then prove that dy/dx=y/x.^{x}sin x , prove that d^{2}y/dx^{2}– 2 dy/dx + 2y = 0Examine continuity of function f(x) = e

^{1/x}-1 / e^{1/x}+1 at x=0sin inverse(a+bcosx/b+acosx)

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

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

^{2}y/dx^{2.plzzz help}diffrentiate cosx.cos2x.cos3x using repeated application of product rule..plss be fast..!!!!!!!!urgent!!!!!!!!

^{y/x}=x, prove that x^{3}d^{2}y/dx^{2 }= (x.dy/dx - y)^{2}if y=e^x + log x/sin 3x, find dy/dx

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}dx^{-1}(cot x/2)If log(x

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

f(x)= sin 2x/ sin 3x , x is not 0

2 , x=0 at x=0

^{-1}( x^{2}- y^{2}/ x^{2}+ y^{2}) = tan^{-1}a, prove that dy/dx = y/xin some cases we take lhl and rhl and in some we dont. why is that so? when do we take lhl and rhl

Find d2y/dx2

^{x }/ x^{8}