Limits
Limit of trigonometric quotient
nta_pyq_2025_apr
Grade 12
Question:
If the function f$(x) = tan(tan$$x)-sin(sin$x) is continuous at$x = 0$, then f (0) is equal to ________ tan$x-sin$x
Step-by-Step Solution
Key Concept: Expand the expression near the limiting point using the appropriate standard trigonometric, logarithmic, or exponential approximation.
tan(tan$x)-tan$x tan x tan$x-sin$x sin$x-sin(sin$x) sin x + + 3 3 tan x$x_{3}$$x_{3}$sin x$x_{3}$limx$\to$0 (2) tan$x-sin$x$x_{3}$1 1 1 + + 3 2 6 = = 2 1 2
Correct Answer: 2