Question

Find the value of the constant k so that the function given below is continuous at x=0.

$f\left(x\right)=\frac{1-\cos 2x}{2x^2},x\ne 0$

$f\left(x\right)=k,x=0$

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is B 1

$f\left(x\right)$ is continuous at $x=0$.

Thus,

$li{m}_{x\to 0}\frac{1-\cos 2x}{2x^2}=k$

$li{m}_{x\to 0}\frac{2{\sin }^{2}x}{2x^2}=k$

$li{m}_{x\to 0}(\frac{\sin x}{x}{)}^2=k$

$k^2=1⟹k=1$