Limits, Continuity & Differentiability
Trigonometric and Logarithmic Limit
nta_pyq_2023_apr
Grade 12
Question:
$\displaystyle\lim_{x\to0}\left(\dfrac{1-\cos^2(3x)}{\cos^3(4x)}\right)\left(\dfrac{\sin^3(4x)}{(\ln(2x+1))^5}\right)$ is equal to
Step-by-Step Solution
Key Concept: Use standard limits: $\lim_{x\to0}\frac{1-\cos ax}{x^2}=\frac{a^2}{2}$, $\lim\frac{\sin bx}{x}=b$, $\lim\frac{\ln(1+cx)}{x}=c$.
$\frac{2\cdot9\cdot64}{32}=18$.
Correct Answer: 3