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Syllabus

what is the value of

eraised to infinity ?Find the sum: 7+77+777+.....upto n terms.

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

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

^{2 }^{-1}[(a+bcosx)/(b+acosx)] w.r.t xFIND VALUES OF a , b

If x = sint and y = sinpt prove that :

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

^{x}-5^{x}-2^{x}+1/x^{2}when x tends to 0.if sqrt(1-x

^{2)}+ sqrt(1-y^{2}) = a (x-y) prove dy/dx=sqrt((1-y^{2})/(1-x^{2}))find the derivative of cos root x wrt x from first principle??

if x

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

^{2})y_{2}-xy_{1}-a^{2}y = 0if y= [log(x+root x

^{2}+1)]^{2 }show that (1+x^{2}) d^{2}y/dx^{2}+xdy/dx =2if y=e^x + log x/sin 3x, find dy/dx

if y= sin inverse [ 5x +12 root 1-x2 by 13 find dy by dx

f(x) ={ ax+b if x <0

2sinx+3cosx if x>= 0

is differentiable at x = 0

^{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

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

^{-1}[ (root 1 - x^{2}) / x ]^{}w.r.t. cos^{-1}[2x (root 1 - x^{2})].Thumbs up will be given

if e

^{x}+e^{y}=e^{x+y},prove that dy/dx+e^{y-x}=0$\mathbf{4}\mathbf{.}\underset{h\to 0}{\mathrm{lim}}\frac{\mathrm{tan}\left(a+2h\right)-2\mathrm{tan}\left(a+h\right)+\mathrm{tan}a}{{h}^{2}}isequalto\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(A\right)\mathrm{tan}a\left(B\right){\mathrm{tan}}^{2}a\left(C\right)seca\left(D\right)2\left(se{c}^{2}a\right)\left(\mathrm{tan}a\right)$

^{y}+y^{x}=cfind 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

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

√x +bx^2 - √x / b x^3/2 , x >0

function is continuous at x=0

Q. What is the degree of infinity raised to the power of one?

c ,x=0

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

^{3}, x>0 is constant at x=0^{}Examine continuity of function f(x) = e

^{1/x}-1 / e^{1/x}+1 at x=0if Cosy= xCos(a+y), show that dy/dx= cos

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

^{-1}(cot x/2)if e

^{x}+e^{y}=e^{x+y},prove that dy/dx= -e^{y-x}If f(x) = {(3+x)/(1+x)}

^{2+3x}, find f '(0).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.^{2}+ qx + r where p not equal to 0 and x belongs to [a,b]if siny= xsin(a+y),then prove that dy/dx=sin^2(a+y)/sin a

By first principal.

Q. â€‹Find least positive integer x satisfying

276x +128 $\equiv $ 4 (mod 7)

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

(√x)/√16+root of x-4 }

^{3}differentiate wrtx

under root (1+sinx/1-sinx)

P T d square y÷d x square =

-2a square s square ÷y raised to 5

types of partial fraction

tan

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

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

y=log( cosec

^{x) }find dy/dxIf x = a (θ - sin θ) and y = a (1 - cos θ), find y

_{2}at θ = .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 }.

How to find dy/dx when y=cos-1[2cosx+3sinx]/root13 ??????

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) .

y=tan

^{-1}(xsina/1-xcosa)If y = sin (sin x), prove that

d

^{2}y/dx^{2}+ (tan x) dy/dx + y cos^{2}x = 0.41) If y = sin {2tan

^{-1}{ root over 1-x /1+x } } , find dy/dx]

If x

^{p}y^{q}=(x+y)^{p+q}, then prove that dy/dx=y/x.^{2}-7x+3)^{5/2}w.r.t xif

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.

$f\left(x\right)=\left\{\begin{array}{ll}2{x}^{2}-3,& ifx\le 1\\ 5,& ifx1\end{array}\right.$

continuous at x = 0? What about its continuity at x = 1 and 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}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}dxf(x)= x

^{3}- 6x^{2}+11x -6 on [1,-3]If log(x

^{2}+y^{2})=2tan^{-1(}y/x), then show that dy/dx=x+y/x-y.If x= 3sint-sin3t, y= 3cost-cos3t, find d^2y/dx^2 at t=pi/3

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

a+sinx/1+asinx?

^{-1}( x^{2}- y^{2}/ x^{2}+ y^{2}) = tan^{-1}a, prove that dy/dx = y/xshow that f(x) = |x| is a continuous function everywhere?

Find d2y/dx2

Find dy/dx , when y = (sin x + x

^{2}) /^{}(cot 2x) .