1
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Change Language
Domain of definition of the function f(x) = $${3 \over {4 - {x^2}}}$$ + $${\log _{10}}\left( {{x^3} - x} \right)$$, is
A
(-1, 0)$$ \cup $$(1, 2)$$ \cup $$(2, $$\infty $$)
B
(1, 2)
C
(-1, 0) $$ \cup $$ (1, 2)
D
(1, 2)$$ \cup $$(2, $$\infty $$)
2
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$\mathop {\lim }\limits_{x \to 0} {{\log \left( {3 + x} \right) - \log \left( {3 - x} \right)} \over x}$$ = k, the value of k is
A
$$ - {2 \over 3}$$
B
0
C
$$ - {1 \over 3}$$
D
$${2 \over 3}$$
3
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$f(a) = g(a) = k$$ and their nth derivatives
$${f^n}(a)$$, $${g^n}(a)$$ exist and are not equal for some n. Further if

$$\mathop {\lim }\limits_{x \to a} {{f(a)g(x) - f(a) - g(a)f(x) + f(a)} \over {g(x) - f(x)}} = 4$$

then the value of k is
A
0
B
4
C
2
D
1
4
AIEEE 2003
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\mathop {\lim }\limits_{x \to {\pi \over 2}} {{\left[ {1 - \tan \left( {{x \over 2}} \right)} \right]\left[ {1 - \sin x} \right]} \over {\left[ {1 + \tan \left( {{x \over 2}} \right)} \right]{{\left[ {\pi - 2x} \right]}^3}}}$$ is
A
$$\infty $$
B
$${1 \over 8}$$
C
0
D
$${1 \over 32}$$
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