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Syllabus

what is the value of

eraised to infinity ?_{a}b^{3}= log_{10}27 .ln10 then find a relation bet a and b such that a not equals bFind the sum: 7+77+777+.....upto n terms.

If x

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

^{2 }(a) at least one root of f (x) = 0

(b) at most one root of f (x) = 0

(c) exactly one root of f (x) = 0

(d) at most one root of f" (x) = 0

FIND VALUES OF a , b

^{2})^{3/2}, show that (1-x^{2}) d^{2}y/dx^{2}+ x dy/dx + 3y = 0If x = sint and y = sinpt prove that :

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

^{log2}^{x}, prove that dy/dx=2xif sqrt(1-x

^{2)}+ sqrt(1-y^{2}) = a (x-y) prove dy/dx=sqrt((1-y^{2})/(1-x^{2}))if y = e^theta (2 sin theta + sin 2 theta), x = e^theta (2 cost theta + cos 2 theta), find dy/dx

if x

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

f(x)={ √5x+2 - √4x+4/ x-2.

x (not equal) 2

k. x =2 }

if y= [log(x+root x

^{2}+1)]^{2 }show that (1+x^{2}) d^{2}y/dx^{2}+xdy/dx =2For 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 y= sin inverse [ 5x +12 root 1-x2 by 13 find dy by dx

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?

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

prove that

dy/dx= 2 - x/y

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

^{4}, u = 1/v , v = 5x^{2}+2x+6c ,x=0

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

^{3}, x>0 is constant at x=0^{}Q. What is the degree of infinity raised to the power of one?

if Cosy= xCos(a+y), show that dy/dx= cos

^{2}(a+y)/sin(a)f(x) ={ ax+b if x <0

2sinx+3cosx if x>= 0

is differentiable at x = 0

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

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

if e

^{x}+e^{y}=e^{x+y},prove that dy/dx= -e^{y-x}Differentiate tan

^{-1}[ x / {√(1 - x^{2})} ] w.r.t. cos^{-1}(2x^{2}- 1).[ Taking x = sin theta: ]

integration of root tanx ?

^{2}-4a^{2})^{1/2}(x^{2}-a^{2}) then dy/dx isshow 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.^{3}+4, t= x^{2 }+ 2xif siny= xsin(a+y),then prove that dy/dx=sin^2(a+y)/sin a

^{-1}[x*sqrt(1-x) - sqrt(x)*sqrt(1-x^{2})] find dy/dx(2tanx/tanx +cosx)^2

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

(√x)/√16+root of x-4 }

^{-1}y = 2log(x+1) show that (x+1)^{2}y + (x+1)y +4y = 0differentiate wrtx

under root (1+sinx/1-sinx)

types of partial fraction

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

tan

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

^{2}+ 2 / 1 + 4x^{2})^{I}(x) when f(x)=10^{x}+x^{10}+10x+10^{10}If x = a (θ - sin θ) and y = a (1 - cos θ), find y

_{2}at θ = .if y=cos

^{-1}(3+5cosx)/(5+3cosx) find dy/dx?????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) .

^{x/x-y }= a ,prove that ydy/dx + x = 2yIf y = sin (sin x), prove that

d

^{2}y/dx^{2}+ (tan x) dy/dx + y cos^{2}x = 0.Differentiate with respect to x:

Root under cosec( x

^{3}+ 1)The answer given in the book is : - 3/2 x

^{2}root under cosec ( x^{3}+ 1) . cot ( x^{3}+ 1)_{x6 + root 1-y}^{6 = }^{a3(x3-y3). }prove dy/dx = x^{2}/y^{2}*wholeroot 1-y^{6}/1-x^{6}^{-1}[(a+bcosx)/(b+acosx)] w.r.t xIf x

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

^{1/x}-1 / e^{1/x}+1 at x=0what is dy/dx when y=tan-1[5ax/a2-6x2]

here 2 represents the square

if

xy_{+}_{y}x =_{a}b find dy/dx^{-1}(cot x/2)If 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}Find the value of k if f(x) = (root (1+kx) – root (1-kx))/x , -1<=x <0

= (2x + 1)/(x-1) , 0<=x< 1

is continuous at x=0.

^{y/x}=x, prove that x^{3}d^{2}y/dx^{2 }= (x.dy/dx - y)^{2}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 y=sin(tan

^{-1}2x) prove that dy/dx=2/(1+4x^{2})^{3/2}^{}If log(x

^{2}+y^{2})=2tan^{-1(}y/x), then show that dy/dx=x+y/x-y.f(x)= { 5x-4 if 0 { 4x2 - 3x if 1 { 3x + 4 if x > equal to 2

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

^{(2log x+7)}then (dy)/(dx)=Please Don't Give A LinkPlease Solve It

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/xFind d2y/dx2