Question

$Lt_{x \to 0}\frac{e^{x^2}-cos x}{sin^2x}=$

• A. 3
• B. 3/2
• C. 5/4
• D. 2

Hint:

Series expansion is often faster than L'Hôpital's rule for trigonometric/exponential combinations.

Answer 1

The Correct Option is B

Step 1: Concept Use standard limits or expansion/L'Hôpital's Rule for $0/0$ forms.

Step 2: Meaning $e^{x^2} \approx 1 + x^2$ and $\cos x \approx 1 - x^2/2$.

Step 3: Analysis Numerator: $(1+x^2) - (1-x^2/2) = 3x^2/2$. Denominator: $\sin^2 x \approx x^2$.

Step 4: Conclusion Limit: $\frac{3x^2/2}{x^2} = 3/2$. Final Answer: (B)