1
WB JEE 2008
MCQ (Single Correct Answer)
+1
-0.25

A function f(x) is defined as follows for real x

$$f(x) = \left\{ {\matrix{ {1 - {x^2}} & , & {for\,x < 1} \cr 0 & , & {for\,x = 1} \cr {1 + {x^2}} & , & {for\,x > 1} \cr } } \right.$$

Then

A
f(x) is not continuous at x = 1
B
f(x) is continuous but not differentiable at x = 1
C
f(x) is both continuous and differentiable at x = 1
D
f(x) is continuous everywhere but differentiable nowhere.
2
WB JEE 2009
MCQ (Single Correct Answer)
+1
-0.25

Let $$f(x) = {{\sqrt {x + 3} } \over {x + 1}}$$, then the value of $$\mathop {\lim }\limits_{x \to - 3 - 0} f(x)$$ is

A
0
B
does not exist
C
1/2
D
$$-$$1/2
3
WB JEE 2009
MCQ (Single Correct Answer)
+1
-0.25

$$f(x) = x + |x|$$ is continuous for

A
x $$\in$$ ($$-$$ $$\infty$$, $$\infty$$)
B
x $$\in$$ ($$-$$ $$\infty$$, $$\infty$$) $$-$$ {0}
C
only x > 0
D
no value of x
4
WB JEE 2009
MCQ (Single Correct Answer)
+1
-0.25

The value of $$\mathop {\lim }\limits_{x \to 1} {{\sin ({e^{x - 1}} - 1)} \over {\log x}}$$ is

A
0
B
e
C
1/e
D
1
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