TIFR ECE 2021 | Question: 3

Question

Consider the following statements:

1. $\lim _{x \rightarrow 0} \frac{\sin x}{x}=1$.
2. $\lim _{x \rightarrow 0} \frac{1-\cos x}{x^{2}}=1$.
3. $\lim _{x \rightarrow 0} \frac{1-\cos x}{x}=1$.

Which of the following is $\text{TRUE?}$

• A. Only Statement $1$ is correct.
• B. Only Statements $1$ and $2$ are correct.
• C. Only Statements $1$ and $3$ are correct.
• D. All of Statements $1, 2,$ and $3$ are correct.
• E. None of the three Statements $1,2,$ and $3$ are correct.