Limits
Composite Limit
MMTS_Full_Test_03
Grade 12
Question:
Consider: Statement-1: If $f(x)$ and $g(x)$ have limits at $x=a$, then $\text{Lt}_{x\to a}[f(g(x))]=\left[\text{Lt}_{x\to a}f(g(x))\right]$ ($[\cdot]$ denotes G.I.F). Statement-2: A function may fail to have a limit at a point in its domain but functional value at $x=a$ exists.
Only S-I is true
Only S-II is true
Both S-I and S-II are True
Both S-I and S-II are false
Step-by-Step Solution
Key Concept: S1: Limit of GIF $\ne$ GIF of limit in general; S2: standard fact
S1) False. S2) True. Only S-II.
Correct Answer: 2