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Syllabus

what is the value of

eraised to infinity ?If x

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

(ii) d

^{2}y/dx^{2}= 0Find the sum: 7+77+777+.....upto n terms.

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

If x

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

^{2 }^{p}y^{q}=(x+y)^{p+q},then prove that d^{2}y/dx^{2}=0FIND 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 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 !!

^{-1}[(a+bcosx)/(b+acosx)] w.r.t xif 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^{2}g(x) and g(1) = 6 ,g'(1) = 3 find the value of f'(1)k.c.sinha exercise-13.1 question-

^{2 /}a^{2}+ y^{2/}b^{2}= 1 show that d^{2}y/ dx^{2}= - b^{4}/a^{2}y^{3}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 the continuity of the function F(x)= 1/ (x-3) for all x belongs to R.

if e

^{x}+e^{y}=e^{x+y},prove that dy/dx+e^{y-x}=0if y=x^e^-x^2,find dy/dx

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

If f(x) = {(3+x)/(1+x)}

^{2+3x}, find f '(0).√x +bx^2 - √x / b x^3/2 , x >0

function is continuous at x=0

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

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)prove that

dy/dx= 2 - x/y

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

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

(√x)/√16+root of x-4 }

if e

^{x}+e^{y}=e^{x+y},prove that dy/dx= -e^{y-x}^{3}and y =2at^{2}/(1+t^{3})^{2}then dy/ dx =?integration of root tanx ?

x

^{2}/ a^{2}+ y^{2}/ b^{2}= 1The answer: - b

^{2}x / a^{2}yshow 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.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 }.

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

^{3}^{x}^{ ^ a ^ x ……. infinity}, prove that dy/dx = y^{2}log y / x[ 1 – y ( log x ) ( log y ) ]differentiate wrtx

under root (1+sinx/1-sinx)

^{2}+ qx + r where p not equal to 0 and x belongs to [a,b]types of partial fraction

differentiate of e

^{sin x }+ (tan x )^{x}tan

^{-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 = .^{x }+ sin^{-1 }root (3x) with respect to xf(x) = x

^{2}sin(1/x), if x is not equal to 00, if x = 0

Discuss the continuity of the function 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) .

If y = sin (sin x), prove that

d

^{2}y/dx^{2}+ (tan x) dy/dx + y cos^{2}x = 0.^{2}( x not equal to zero) and k ( x = 0 ). find value of k if f(x) is continuous at x=0_{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.y sec x + tan x + x

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

^{2}x + 2xy )/ ( x^{2}+ sec 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 ki power y +Y ki power x =a ki power b. find dy/dx

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

cot

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

^{2}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}Thumbs up will be given

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 Xp Yq=(x+y)p+q,prove that dy_dx=y_x

If log(x

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

^{3 }= 3ax^{2 }- x^{3}then prove that d^{2}y/dx^{2}= -2a^{2}y^{2}/y^{5}find derivative of y = log {tan(pie/4 + x/2)}

in some cases we take lhl and rhl and in some we dont. why is that so? when do we take lhl and rhl

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