what is the value of e raised to infinity ?

if sqrt(1-x²⁾+ sqrt(1-y²) = a (x-y) prove dy/dx=sqrt((1-y²)/(1-x²))

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

Find 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 that

dy/dx=(logx)/{log(xe)}²

if y= [log(x+root x²+1)]² show that (1+x²) d²y/dx² +xdy/dx =2

• if f(x) = 1-sin^3x/3cos^2x if x<pi/2
• a , if x = pi/2 is continous at x = pi/2
• b(1-sinx)/(pi-2x)^2

FIND VALUES OF a , b

If x = sint and y = sinpt prove that :

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

if x^m yⁿ = (x+y)^m+n show that dy/dx= y/x and find d²y/dx²

plzzz help !!

 y=xlog(x/(a+bx)), prove that x^3Xd^2y/dx^2 = (x(dy/dx)-y)^2

 Examine continuity of function     f(x) = e^1/x-1 / e^1/x+1   at  x=0

k.c.sinha exercise-13.1 question-

1. differentiate sin -1 (2x+1.3x)/1+36x.
2. all in powers.

If y=tan^-1[5ax/a²-6x²], prove that :

dy/dx = (3a/a²+px²) + (2a/a²+4x²)

Differentiate tan^-1 [ (root 1 - x²) / x ]w.r.t. cos^-1 [2x (root 1 - x²)].

if e^x+e^y=e^x+y,prove that dy/dx+e^y-x=0

if f(x)= {cos²x -sin²x-1/under root of(x²-1)-1 ,x is not=0

{k ,x=0

is continuous at x=0 ,find k

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) / x³ ,x>0

is continuous at x=0

If y = e^x.tan^-1x,prove that (1+x²)y₂ 2(1-x+x²)y₁ + (1-x²)y = 0

1. if root 1-_{x^{6 + root 1-}y}^{6 = a3(x3-y3).} prove dy/dx = x²/y²*wholeroot 1-y⁶/1-x⁶

if Cosy= xCos(a+y), show that dy/dx= cos²(a+y)/sin(a)

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

 integration of root tanx ?

if e^x+e^y=e^x+y,prove that dy/dx= -e^y-x

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 }.

what is dy/dx when y=tan-1[5ax/a2-6x2]

here 2 represents the square

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

differentiate tan^-1(2x/1-x^2) with respect to sin-¹x (2x/1+x^2)

differentiate wrtx

under root (1+sinx/1-sinx)

types of partial fraction

If x = a (θ - sin θ) and y = a (1 - cos θ), find y₂ at θ = .

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

If y = sin (sin x), prove that

d²y/dx² + (tan x) dy/dx + y cos² x = 0.

If x^py^q=(x+y)^p+q, then prove that dy/dx=y/x.

Find dy/dx : y= cos ^-1 (2^x+1/1+4^x)

if xy _+yx = _ab find dy/dx

If x=tan(1/a logy) Show that (1+x²)d²y/dx² + (2x-a)dy/dx = 0

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

if x=2cost -cos2t and y=2sint -sin2t . find d²y/dx^{2.
plzzz help}

If log(x²+y²)=2tan^-1(y/x), then show that dy/dx=x+y/x-y.

Please solve the following problems.

1. Y = Sin(mSin^-1x) prove that 1-x² - xy^-1 +m²y = 0

2

2. Y = Cosec x + Cot x prove that sin x (d²y ) = y²

dx²

3. If Y = 3cos(log x) + 4sin(log x) show that x² (d²y ) + (dy ) + y = 0

dx² dx

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

if x= 2 cos theta - cos 2 theta and y=2sin theta - sin 2theta then prove that dy/dx = tan (3 theta/2)