if f(x) takes two functions = 1-cos2x/2x2 ( x not equal to zero) and k ( x = 0 ) - Maths - Continuity and Differentiability

Question

if f(x) takes two functions = 1-cos2x/2x​2 ( x not
equal to zero) and k ( x = 0 ) find value of k if f(x) is
continuous at x=0

Mayank · Accepted Answer

f(x)=1-cos 2x2x2k   , x = 0; x≠0Since given function is continuous at x = 0, then      limx→0 fx = f0⇒limx→01-cos 2x2x2 = k⇒limx→02 sin2x2x2 = k⇒limx→0sin xx×limx→0sin xx = k⇒k = 1

if f(x) takes two functions = 1-cos2x/2x​2 ( x not equal to zero) and k ( x = 0 ). find value of k if f(x) is continuous at x=0

if f(x) takes two functions = 1-cos2x/2x² ( x not equal to zero) and k ( x = 0 ). find value of k if f(x) is continuous at x=0