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1
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
Let $$f:R \to R$$ be a positive increasing function with

$$\mathop {\lim }\limits_{x \to \infty } {{f(3x)} \over {f(x)}} = 1$$. Then $$\mathop {\lim }\limits_{x \to \infty } {{f(2x)} \over {f(x)}} = $$
A
$${2 \over 3}$$
B
$${3 \over 2}$$
C
3
D
1
2
AIEEE 2008
MCQ (Single Correct Answer)
+4
-1
Let $$f\left( x \right) = \left\{ {\matrix{ {\left( {x - 1} \right)\sin {1 \over {x - 1}}} & {if\,x \ne 1} \cr 0 & {if\,x = 1} \cr } } \right.$$

Then which one of the following is true?
A
$$f$$ is neither differentiable at x = 0 nor at x = 1
B
$$f$$ is differentiable at x = 0 and at x = 1
C
$$f$$ is differentiable at x = 0 but not at x = 1
D
$$f$$ is differentiable at x = 1 but not at x = 0
3
AIEEE 2007
MCQ (Single Correct Answer)
+4
-1
Let $$f:R \to R$$ be a function defined by

$$f(x) = \min \left\{ {x + 1,\left| x \right| + 1} \right\}$$, then which of the following is true?
A
$$f(x)$$ is differentiale everywhere
B
$$f(x)$$ is not differentiable at x = 0
C
$$f(x) > 1$$ for all $$x \in R$$
D
$$f(x)$$ is not differentiable at x = 1
4
AIEEE 2007
MCQ (Single Correct Answer)
+4
-1
The function $$f:R/\left\{ 0 \right\} \to R$$ given by

$$f\left( x \right) = {1 \over x} - {2 \over {{e^{2x}} - 1}}$$

can be made continuous at $$x$$ = 0 by defining $$f$$(0) as
A
0
B
1
C
2
D
$$-1$$
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