Question 2Let f and g be real valued functions defined on interval (–1, 1) such that g(x) is continuous, g(0) ≠ 0, g'(0) = 0, g(0) ≠ 0, and f(x) = g(x) sin x.
Statement-1 : lim(x-->0) [g(x) cot x – g(0) cosec x] = f (0) and
Statement-2 : f '(0) = g(0)Options1. Statement-1 is True, Statement-2 is True; statement-2 is a correct explanation for statement-12. Statement-1 is True, Statement-2 is True; statement-2 is NOT a correct explanation for statement-13. Statement-1 is True, Statement-2 is False4. Statement-1 is False, Statement-2 is True
Question 2
Let f and g be real valued functions defined on interval (–1, 1) such that g(x) is continuous, g(0) ≠ 0, g'(0) = 0, g(0) ≠ 0, and f(x) = g(x) sin x.
Statement-1 : lim(x-->0) [g(x) cot x – g(0) cosec x] = f (0) and
Statement-2 : f '(0) = g(0)
Statement-1 : lim(x-->0) [g(x) cot x – g(0) cosec x] = f (0) and
Statement-2 : f '(0) = g(0)
Options
1. Statement-1 is True, Statement-2 is True; statement-2 is a correct explanation for statement-1
2. Statement-1 is True, Statement-2 is True; statement-2 is NOT a correct explanation for statement-1
3. Statement-1 is True, Statement-2 is False
4. Statement-1 is False, Statement-2 is True
shashank raom , 10 Years ago
Grade 12
