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Syllabus

what is the value of

eraised to infinity ?y sec x + tan x + x

^{2}y = 0The answer: -( y sec x tanx + sec

^{2}x + 2xy )/ ( x^{2}+ sec x )Find the sum: 7+77+777+.....upto n terms.

^{x}^{ ^ a ^ x ……. infinity}, prove that dy/dx = y^{2}log y / x[ 1 – y ( log x ) ( log y ) ]If x

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

^{2 }FIND VALUES OF a , b

if y= [log(x+root x

^{2}+1)]^{2 }show that (1+x^{2}) d^{2}y/dx^{2}+xdy/dx =2If 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}))Thumbs up will be given

if x

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

cot

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

^{2}K, 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 slopetan

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

^{2})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=log t + sin t, y = e^t + cost t, find dy/dx

Differentiate tan

^{-1}[ (root 1 - x^{2}) / x ]^{}w.r.t. cos^{-1}[2x (root 1 - x^{2})].find the derivative of cos root x wrt x from first principle??

if e

^{x}+e^{y}=e^{x+y},prove that dy/dx+e^{y-x}=0Differentiate w.r.t. x : y = tan

^{-1}[ (under root 1 + a^{2}x^{2}) - 1 / ax ]^{-1}[(a+bcosx)/(b+acosx)] w.r.t xfind 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

Examine the continuity of the function F(x)= 1/ (x-3) for all x belongs to R.

√x +bx^2 - √x / b x^3/2 , x >0

function is continuous at x=0

if x=a(1+t

^{2})/(1-t^{2}) , y=(b*2t)/(1-t^{2}) find dy/dx ?c ,x=0

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

^{3}, x>0 is constant at x=0^{}^{x/x-y }= a ,prove that ydy/dx + x = 2yif Cosy= xCos(a+y), show that dy/dx= cos

^{2}(a+y)/sin(a)x

^{2}+ y^{2}= log( xy)The answer: y(1 - 2x

^{2}) / x (2y^{2}- 1)show that f(x) =|x-2| is continuous but not differentiable at x=2. Please reply!!URGENT!!!

^{2}and y = 3 + 2 log t / t , show that dy/dx = tif e

^{x}+e^{y}=e^{x+y},prove that dy/dx= -e^{y-x}integration of root tanx ?

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.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

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?

if x2 + y2 = t + 1/t and x4 +y4 = t2 + 1/t2, then prove tht dy/dx = 1/ x3y

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

(√x)/√16+root of x-4 }

prove that the greatest integer function x is continuous at all points except at integer points

differentiate wrtx

under root (1+sinx/1-sinx)

types of partial fraction

tan

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

^{2}+ 2 / 1 + 4x^{2})If y = sin

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

_{2}at θ = .if sq.root (1-x

^{4}) + sq.root(1-y^{4})= a(x^{2}- y^{2}) prove thatdy/dx= [sq.root(1-y

^{4) }* x] / [sq.root (1-x^{4}) * y ]^{2 /}a^{2}+ y^{2/}b^{2}= 1 show that d^{2}y/ dx^{2}= - b^{4}/a^{2}y^{3}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.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}dxprove that

dy/dx= 2 - x/y

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

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

xy_{+}_{y}x =_{a}b find dy/dxExamine continuity of function f(x) = e

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

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

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

If log(x

^{2}+y^{2})=2tan^{-1(}y/x), then show that dy/dx=x+y/x-y.if f(x)= {cos

^{2}x -sin^{2}x-1/under root of(x^{2}-1)-1 ,x is not=0{k ,x=0

is continuous at x=0 ,find k

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

Differentiate with respect to x:

sin 5x cos 3x

The answer given in the book is : 4 cos 8x + cos 2x

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

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