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CBSE
Mathematics
L-hospital's rule
If $f\left( 5 \right) = 7$ and $f'\left( 5 \right) = 7$ then $\mathop {\lim }\limits_{x \to 5} \dfrac{{xf\left( 5 \right) - 5f\left( x \right)}}{{x - 5}}$ is given by
$\left( a \right)35 \\ \left( b \right) - 35 \\ \left( c \right)28 \\ \left( d \right) - 28 \\$
CBSE
Mathematics
L-hospital's rule
Find the limit of the following:
(1) $\mathop {\lim }\limits_{x \to 2} \dfrac{{\sqrt {3 - x} - 1}}{{2 - x}}$
(2) $\mathop {\lim }\limits_{x \to 0} \dfrac{{{3^{2x}} - {2^{3x}}}}{x}$
CBSE
Mathematics
L-hospital's rule
Find the limit as $x$ approaches infinity of $x\sin \left( {\dfrac{1}{x}} \right)$

CBSE
Mathematics
L-hospital's rule
Evaluate $$\mathop {\lim }\limits_{x \to 0} \,\,\dfrac{{1 - \cos x}}{{{x^2}}}$$?
CBSE
Mathematics
L-hospital's rule
What is $\mathop {\lim }\limits_{h \to 0}$ $\dfrac{{\sqrt {2x + 3h} - \sqrt {2x} }}{{2h}}$ equal to ?
(A) $\dfrac{1}{{2\sqrt {2x} }}$
(B) $\dfrac{3}{{\sqrt {2x} }}$
(C) $\dfrac{3}{{2\sqrt {2x} }}$
(D) $\dfrac{3}{{4\sqrt {2x} }}$

CBSE
Mathematics
L-hospital's rule
If $\mathop {\lim }\limits_{x \to 2} \dfrac{{{x^n} - {2^n}}}{{x - 2}} = 448$, then $n =$
CBSE
Mathematics
L-hospital's rule
What is the limit of $\dfrac{{\sin \left( {2x} \right)}}{{{x^2}}}$ as $x$ approaches 0?

CBSE
Mathematics
L-hospital's rule
Evaluate the limit x tends to zero $\log (1 + 5x)$ whole divide by x.

CBSE
Mathematics
L-hospital's rule
Let $f\left( \beta \right) = \mathop {\lim }\limits_{\alpha \to \beta } \dfrac{{{{\sin }^2}\alpha - {{\sin }^2}\beta }}{{{\alpha ^2} - {\beta ^2}}}$ , then $f\left( {\dfrac{\pi }{4}} \right)$ is greater than-
A. $\mathop {\lim }\limits_{x \to \infty } \dfrac{{1 - {{\cos }^3}x}}{{x\sin 2x}}$
B. $\mathop {\lim }\limits_{x \to \infty } \dfrac{{\cot x - \cos x}}{{{{\left( {\pi - 2x} \right)}^3}}}$
C. $\mathop {\lim }\limits_{x \to \infty } \left( {\cos \sqrt {x + 1} - \cos \sqrt x } \right)$
D. $\mathop {\lim }\limits_{x \to a} \dfrac{{\sqrt {a + 2x} - \sqrt {3x} }}{{\sqrt {3a + x} - 2\sqrt x }}$ where $a > 0$
CBSE
Mathematics
L-hospital's rule
How do you find the limit of $x\left( {{e}^{-x}} \right)$ as x approaches infinity using L’Hospital rule?
CBSE
Mathematics
L-hospital's rule
How can I find the limit of $\dfrac{{\sqrt {16 - x} - 4}}{x}$ as it approaches 0?
CBSE
Mathematics
L-hospital's rule
How do you find the limit of ${x^{2x}}$ as x approaches 0?
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