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Syllabus

If y= sin

^{-1}x/(1-x^{2)1/2 show that (1-x2)d2y/dx2 - 3x dy /dx -y =0}If x sin ( A + y) + sinA cos (A + y) = 0, prove that dy/dx = [ sin

^{2 }(a + y) ] / sin a.Differentiate

if y= xsin

^{-1}x /(1-x^{2})^{1/2}^{2}=9p(9-y) and X^{2}=p(y+1) cut each other at right angleIf X=2cost-cos2t and Y=2sint-sin2t, then prove that

dy/dx=tan(3t/2)

If y

^{3 }+ x^{3 }-3axy = 0, PT d^{2}y/dx^{2 }= -2a^{3}xy/(y^{2}-ax)^{3}If y=e

^{acos-1x }; -12)d^{2}y/dx^{2 }- x dy/dx - a^{2}y =0^{}^{}find dy/dx

tan(x+y)+tan(x-y)=1

^{3}log(1/x), then prove that x (d^{2}y)+(dx^{2}) - 2 dy/dx+3x^{2}=0.If tan

^{-1}[ (x^{2}- y^{2})/ (x^{2}+ y^{2}) ] = a ; prove that dy/dx = x( 1 - tanA) / y ( 1 + tanA)Show that the function f defined as follows, is continuous at

x=2. but not differentiable there at: f(x)={3x-2, 0<x<=12x^{2}-x, 1<x<=25x-4, x>2}^{-1}(3sinx+4cosx/5).if x=a{(1+t

^{2)}/(1-t^{2})} and y=2t/(1-t^{2}) find dy/dx.differentiate y= (x)

^{cosx}+ (cosx)^{sinx}Differentiate w.r.t x:

log(cosecx-cotx)

f(x) = max. (sin x , cos x ) for all x belongs to R . Then number of critical points belongs to ( -2pi , 2pi ) is/ are

(a) 5 (b) 4

(c) 7 (d) none of these

if y(x

^{2}+1)^{1/2}= log ((x^{2}+1) - x)show that

(x

^{2}+1) dy/dx + xy + 1 =0If f(x) = log

_{x}(log_{e}x), then f`(x) at x=e is equal to???f(x)={1-cos4x/8x

^{2}, x not equal to 0k, x=0

is continuous at x=0.

What is RHD and LHD explain with a n example.

f(x)={xtan-1(1/x), x≠0

{0, x=0 at x=0.

Show that f(x)=

{ (e

^{1/x}-1)/(e^{1/x}+1) , x not equal to 0 is discontinuous at x=0.0 , x=0

log (x

^{2}+x +1/x^{2}- x + 1){ sinx/x +cosx, x not equal to 0

2, x=0.

Show that f(x) is continuous at x=0.

If y=(cosx)

^{lnx }+(lnx)^{x }find dy/dx

Differentiate sin-

^{1}x w.r.t log( 1+x )^{-1}[3x + (4root(1-x^{2}))/5] find dy/dxf(x) = x

^{3}+ bx^{2}+ax on [1,3] .Rolles theorem holds for c= 2 + 1/3^{1/2 }.Find a and bshow that every constant function is continuous?

how does a kink in the graph of the function represents the point of non-differentiability? explain in details with examples

If x sin ( A + y) + sinA cos (A + y) = 0, prove that dy/dx = [ sin

^{2}(a + y)] / [ sin (a + y) - ycos ( a + y ) ]Are the proofs of theorems important from the exam point of view? I mean, will we be asked to prove theorems given in the maths textbook in the boards?

If siny + e

^{ - x cos y}= e then dy/dx at (1,╥)is......??^{3.}solve with the help of sandwich theorem .Sir i do not agree to you completely...

It is said that log of x to base x is equal to 1 then why is it not log of 1 to base 1 is equal to 1?????

and i did not understand the reasoning behind your saying 0/0 for it...

If y^1/n + y^-1/n = 2x, the (1-x^2)y2 + xy1 =

1) -n^2y 2) n^2y 3) 0 4) none of these

Pls give detailed solution and its explaination :

1) If f(x) = 1/3 { f( x+1) + 5/ f( x+2) } and f(x) 0 for all x belongs to R then lim x-- oo f(x) = ???

a) 0 b) (2/5)^1/2 c) ( 5/2 )^1/2 d) infintiy

2) If k = lim x --- oo ( E1000k =1 ( x+k)m / xm + 101000 ) and ( m 101) then k = ???

a) 10 b) 102 c) 103 d) 104

(* oo implies infinity. E implies summation running from k =1 to 1000)

if y= log tan ( pi/4+ x/2)

show that dy/dx - sec x = 0

^{2}+ 1],[x] denoting greatest integer function ,is discontinuous at..........points.If x^{m}y^{n}= (x+y)^{m+n}prove thatdy/dx=y/x?let g(x) be the inverse of an invertible function f(x) which is derivatable at x=3. If f(3)=9 and f'(3)=9, write the calue of g'(9).

x

^{m}sin(1 / x) , x is not equal to 0Show that the function ƒ(x) = is

0 , x = 0

(i) differentialble at x = 0, if m1

(ii) continous but not differentiable at x = 0, if 0

(iii) neither continous nor differentiable, if m ≤ 0

dy/dx of y= log(sinx/1+cosx)

wat is log00??????

also log1 to any base is zero, then log 1 to base 1 is what???

If f(x) = (log

_{cot x }tanx) (log_{tan x}cot x)^{-1}+ tan^{-1}(4x / 4 - x^{2}), then f`(2) is equal to????^{x}P.T d^{2}y/dx^{2}- 1/y(dy/dx)^{2 }- y/x =0pl can some one differentiate y=sin(sin(log 3x))

given that for the function f(x)=x3-6x2+px+q on[1,3] , Rolles theorem holds with c=2+ 13 . Find the values p and q.

If y=e

^{x}(sinx+cosx)Prove that: d

^{2}y/dx^{2}- 2ydy/dx + 2y =0If y

^{x}=e^{y-x}. prove that dy/dx=(1+log y)^{2}/log y