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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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