If the function f(x)={{:((sin x)/(x) + c...

If the function `f(x)={{:((sin x)/(x) + cos x", if " x ne 0 ), (k", if " x =0 ):}`
is continuous at x=0, then find the value of k.

Verified by Experts

The correct Answer is:

`kappa = 2`

Similar Questions

Explore conceptually related problems

Prove that f (x) =|x| is continuous at x =0

If sin(3x+10)=cos(x+24) then find the value of x.

Find the value of a for which f(x)={(sin^2(ax)/(x^2), "" xne0),(1, x=0 ""):} is continuous at x = 0

Find the value of a for which f(x)={((1-cos4x)/(8x^2), "" xne0),(a, x=0 ""):} is continuous at x = 0

f(x)={(x^2+2x, "" xle0,),(ax+b, "" x >0,):} is continuous and differentiable at x =0, find the values of a and b

Find the value of kappa , so that the function f(x)={{:((x^(3)+x^(2)-16x+20)/((x-2)^(2))","," if" x ne2,),(kappa","," if" x=2,):} is continous at x=2

Find the value of k for which f(x)={((kcosx)/(pi-2x), "" xnepi/2),(3",", ""x=pi/2):} is continuous at x=1

If f(x) = k, a constant, find the value of Deltaf(x) .