Limits
Trigonometric limit with powers
nta_pyq_2025_apr
Grade 12
Question:
If Lim , then 96 log p is equal to ______ tan x x 2 x$\to$0 ($) = p$e x
Step-by-Step Solution
Key Concept: Expand the expression near the limiting point using the appropriate standard trigonometric, logarithmic, or exponential approximation.
tan x$x_{2}$$P = lim$x$\to$0 ( ) (32) x tan$x-x$limx$\to$0 ( ) $\Rightarrow$$P = e$$x_{3}$3 5 x 2x (x+ + +$\ldots$.$.-x)$3 15 limx$\to$0 = e$x_{3}$$1/3 = e$p 1 ∴ 96$log = 96$$\times$ = 32 e 3
Correct Answer: 32