what is the value of e raised to infinity ?

Find the sum:  7+77+777+.....upto n terms.

If x^y =e^x-y show that

dy/dx=(logx)/{log(xe)}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 sqrt(1-x²⁾+ sqrt(1-y²) = a (x-y) prove dy/dx=sqrt((1-y²)/(1-x²))

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

plzzz help !!

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

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

k.c.sinha exercise-13.1 question-

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

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