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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}^{-1}(3sinx+4cosx/5).If x sin ( A + y) + sinA cos (A + y) = 0, prove that dy/dx = [ sin

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

if y= xsin

^{-1}x /(1-x^{2})^{1/2}Differentiate sin-

^{1}x w.r.t log( 1+x )^{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)

f(x)={xtan-1(1/x), x≠0

{0, x=0 at x=0.

If y

^{3 }+ x^{3 }-3axy = 0, PT d^{2}y/dx^{2 }= -2a^{3}xy/(y^{2}-ax)^{3}{ sinx/x +cosx, x not equal to 0

2, x=0.

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

If y=e

^{acos-1x }; -12)d^{2}y/dx^{2 }- x dy/dx - a^{2}y =0^{}^{}VERIFY ROLLE THEROEM FOR THE FUNCTION F(X) =X3-3X2+2x in the interval {0,2}

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.The derivative of y = 1 - mod x at x = 0 is ....??

If tan

^{-1}[ (x^{2}- y^{2})/ (x^{2}+ y^{2}) ] = a ; prove that dy/dx = x( 1 - tanA) / y ( 1 + tanA)If y = log

^{n}x, where log^{n}means log log log (repeated n times), then x log x log^{2}x log^{3}x. log^{n-1}x log

^{n}x dy/dx is equal to???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}pl can some one differentiate y=sin(e^x.logx)

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 x=a{(1+t

^{2)}/(1-t^{2})} and y=2t/(1-t^{2}) find dy/dx._{3}(x^{2}+1)/(sin^{2}x - sinx + 0.25)differentiate y= (x)

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

log(cosecx-cotx)

A function f(x) is defined as ,

f(x)={(x

^{2}-x-6)/x-3; if x not =35 ;if x=3.

Show that f(x) is continuous at x=3.

if y(x

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

(x

^{2}+1) dy/dx + xy + 1 =0lim

_{x---0}x^{4}(cot^{4}x-cot^{2}x+1) / (tan^{4}x-tan^{2}x+1)If f(x) = log

_{x}(log_{e}x), then f`(x) at x=e is equal to???if f(x) = sin ( 2pi[pi

^{2}-x] )/5+[x]^{2}, [.] denotes greatest integral function ), then f(x) is(a) discontinuous at some x (b) continuous at all x , but the derivative f'(x) does not exisrs for some x

(c) f'(x) exists for all x , but f'"(x) does not exists (d) f"(x) exists for all x

f(x)={1-cos4x/8x

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

is continuous at x=0.

If y=e

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

^{2}y/dx^{2}- 2ydy/dx + 2y =0What is RHD and LHD explain with a n example.

If y = √1+x / 1-x, then what is the value of dy/dx.

if x = 3sint - sin3t

y = 3cost - cos3t

find d

^{2}y / d^{2}x at x = pi/3Show 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)What is the base change rule in logarithmic?

If siny + e

^{ - x cos y}= e then dy/dx at (1,╥)is......??If y=(cosx)

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

Show that how:lim

_{h}_{→0}e^{tan2h/tan 3h }= e^{ 2/3}^{-1}[3x + (4root(1-x^{2}))/5] find dy/dxx

^{2}^{/3}+ y^{2}^{/3}=a^{2}^{/3}thanks

f(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?

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

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 ) ]f(x)={ 2

^{x+2}-16/4^{x}-16 , x not equal to 2k , x=2

is continuous at x=2.

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?

pl can some one differentiate y=log(x+(x^2+a^2)^1/2)

^{3.}solve with the help of sandwich theorem .If y = log (x + √ a

^{2}+ x^{2}), show that (x^{2}+a^{2}) d^{2}y / dx^{2}+ x dy/dx = 0Sir 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...

lim x tends to 0=(4

^{sinx}-1)^{2}/sin^{2}xprove that 2y=xy' + ln y',where y' denotes dy/dx

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

f(x)={x-4/|x-4| +a,x≤4

a+b,x=4

x-4/|x-4| +b,x≥4

^{2}+ 1],[x] denoting greatest integer function ,is discontinuous at..........points.pl can some one differentiate y=sin(sin(log 3x))

If x^{m}y^{n}= (x+y)^{m+n}prove thatdy/dx=y/x?find the points of discontinuity of the function 'f' given by

f(x)={ |x|+3, x less than or equal to -3;

-2x, x greater than -3 and less than 3;

6x+2, x greater than 3;

Anwer needed ASAP...!!

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}P.T d^{2}y/dx^{2}- 1/y(dy/dx)^{2 }- y/x =0x

^{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

0,x=4

Check whether f(x) is continuous at x=4.

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???

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

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