1
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\mathop {\lim }\limits_{x \to \infty } {\left( {{{{x^2} + 5x + 3} \over {{x^2} + x + 2}}} \right)^x}$$
A
$${e^4}$$
B
$${e^2}$$
C
$${e^3}$$
D
$$1$$
2
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\mathop {\lim }\limits_{x \to 0} {{\log {x^n} - \left[ x \right]} \over {\left[ x \right]}}$$, $$n \in N$$, ( [x] denotes the greatest integer less than or equal to x )
A
has value $$ -1$$
B
has value $$0$$
C
has value $$1$$
D
does not exist
3
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$f\left( 1 \right) = 1,{f^1}\left( 1 \right) = 2,$$ then
$$\mathop {\lim }\limits_{x \to 1} {{\sqrt {f\left( x \right)} - 1} \over {\sqrt x - 1}}$$ is
A
$$2$$
B
$$4$$
C
$$1$$
D
$${1 \over 2}$$
4
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Change Language
$$f$$ is defined in $$\left[ { - 5,5} \right]$$ as

$$f\left( x \right) = x$$ if $$x$$ is rational

$$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$ = - x$$ if $$x$$ is irrational. Then
A
$$f(x)$$ is continuous at every x, except $$x = 0$$
B
$$f(x)$$ is discontinuous at every $$x,$$ except $$x = 0$$
C
$$f(x)$$ is continuous everywhere
D
$$f(x)$$ is discontinuous everywhere
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