Question

Find the value of the constant k so that the function

f(x)= 1-cos 4x/8x² if x is not equal to 0
k when x= 0
is continous at x=0??

Answer 1

K=1.
lim f(x)=k
X-->0-

therefore, lim 1-cos4x/8x^2=sin^2(2x)+cos^2(2x)-cos^2(2x)+sin^2(2x)/8x^2
x-->0
=1/8 lim 2sinj^2(2x)/x^2
x-->0
=1/8*2*lim 4 since(lim x-->0 sinx/x=1)
x-->0

therefore k=1/8*2*4=1