Test on Limits and continuity, Differentiation

AIEEE – Test on unit 8 f(x) =x|x| is is not continuous at x=0 continuous at x=0 continuous and differentiable at x=0 none of these f(x) = is is not differentiable at x=0 is differentiable at x=0 is not continuous but differentiable at x=0 none of these f(x) =is is not continuous but differentiable at x=0 is continuous but not differentiable at x=0 by multiplying with x it becomes differentiable at x=0 none of these 4. is a) 1 b) -1 c)0 d)( 5. is (a) 1 b) ½ (c) – ½ d) none 6. The domain of definition f(x) = is (a) (b) (c ) (d) none of these 7. Let f(x)= |x| + [x]. then f() + f(-) is (a) 6 (b) 7 (c) 0 (d) none of these 8. The range of f(x) = is (a) (b) (c) (0, 1) (d) none of these. 9. The value of (a) is 1 (b) is 0 (c) is -1 d) does not exits 10. The value of for f(x) = to be continuous at x= is (a) 1 (b) ½ (c) -1/2 (d) -1 11. If y = ln (ex cos x + e-x sinx) then the value of is (a) 1 (b) 2 (c) 3 (d) 0 12.