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Syllabus

what is the value of

eraised to infinity ?if sqrt(1-x

^{2)}+ sqrt(1-y^{2}) = a (x-y) prove dy/dx=sqrt((1-y^{2})/(1-x^{2}))if y= sin inverse [ 5x +12 root 1-x2 by 13 find dy by dx

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

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 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

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 !!

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

^{y/x}=x, prove that x^{3}d^{2}y/dx^{2 }= (x.dy/dx - y)^{2}how to differentiate sinx w.r.t logx???

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

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

(√x)/√16+root of x-4 }

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})].Examine continuity of function f(x) = e

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

^{x}+e^{y}=e^{x+y},prove that dy/dx+e^{y-x}=0integration of root tanx ?

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

√x +bx^2 - √x / b x^3/2 , x >0

function is continuous at x=0

Please determine the value of a,b,c for which the function f is continous at x=0,

{(sin(a+1)x +sin x)/x , x<0 }

f(x)= {c , x=0 }

{( (x+bx^2)^(1/2) - x^(1/2))/b(x^(3/2)) , 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)differentiate tan

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

^{2}+ 3x + a , x<1 and bx + 2 , x > 1if e

^{x}+e^{y}=e^{x+y},prove that dy/dx= -e^{y-x}Q1. Find out the points/ points at which the function f(x)= (4-x

^{2})/ (4x-x^{3}) is discontinuous.if siny= xsin(a+y),then prove that dy/dx=sin^2(a+y)/sin a

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

under root (1+sinx/1-sinx)

Find d2y/dx2

types of partial fraction

If y=tan

^{-1}[5ax/a^{2}-6x^{2}], prove that :dy/dx = (3a/a

^{2}+px^{2}) + (2a/a^{2}+4x^{2})show that f(x)=sin 3x/tan 2x if x<0 ,3/2 if x=0 and log(1+3x)/e has power 2x minus1 if x>0 ; is continuous at x=o.

If x = a (θ - sin θ) and y = a (1 - cos θ), find y

_{2}at θ = .cot

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

^{2}tan

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

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

differentiate wrtx

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

2)log

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

^{x}+e^{-x})/(e^{x}-e^{-x})If y = sin (sin x), prove that

d

^{2}y/dx^{2}+ (tan x) dy/dx + y cos^{2}x = 0.aandbso that the function f(x) =^{ x2+3x+a, when x<-1}, is differentiable at x belongs to R._{ bx+2,when x>1}If x

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

what is dy/dx when y=tan-1[5ax/a2-6x2]

here 2 represents the square

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 = 0^{2}+ y^{2}= 1 are at right angles , then x1x2/y2y1 is equal to - a^{4}/b^{4}. prove thisif 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

tan

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

^{2x}/ ( 1 + e^{4x})if x=2cost -cos2t and y=2sint -sin2t . find d

^{2}y/dx^{2.plzzz help}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 f(x) = (1- cos kx)/ x sinx , when x is not equal to 0

1/2 , when x = 0

is continuous at x = 0, find 'k'.

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)}

^{-1}( x^{2}- y^{2}/ x^{2}+ y^{2}) = tan^{-1}a, prove that dy/dx = y/xThumbs up will be given

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

if x= 2 cos theta - cos 2 theta and y=2sin theta - sin 2theta then prove that dy/dx = tan (3 theta/2)

if X ki power y +Y ki power x =a ki power b. find dy/dx