# arrow_back If $\mathrm{f}(9)=9, \mathrm{f}^{\prime}(9)=4$, then $\lim _{x \rightarrow 9} \dfrac{\sqrt{f(x)}-3}{\sqrt{x}-3}$

104 views
If $\mathrm{f}(9)=9, \mathrm{f}^{\prime}(9)=4$, then $\lim _{x \rightarrow 9} \dfrac{\sqrt{f(x)}-3}{\sqrt{x}-3}$

Applying L - Hospitals rule,

$\lim _{x \rightarrow 9} \frac{\dfrac{1}{2 \sqrt{f(x)}} \cdot f^{\prime}(x)}{\dfrac{1}{2 \sqrt{2}}}$

$=\dfrac{\dfrac{f^{\prime}(9)}{\sqrt{f(9)}}}{\dfrac{1}{\sqrt{9}}}$

$=\dfrac{\dfrac{4}{3}}{\dfrac{1}{3}}$

$=4$
by Platinum
(119,128 points)

## Related questions

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve $\lim _{x \rightarrow \pi / 4} \dfrac{\sqrt{2} \cos x-1}{\cot x-1}$
Solve $\lim _{x \rightarrow \pi / 4} \dfrac{\sqrt{2} \cos x-1}{\cot x-1}$Solve $\lim _{x \rightarrow \pi / 4} \dfrac{\sqrt{2} \cos x-1}{\cot x-1}$ ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Solve $\lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^{2}+x-3}$
Solve $\lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^{2}+x-3}$Solve $\lim _{x \rightarrow 1} \dfrac{(2 x-3)(\sqrt{x}-1)}{2 x^{2}+x-3}$ ...
$\lim _{x \rightarrow \pi / 2}(\sec \theta-\tan \theta)=$
$\lim _{x \rightarrow \pi / 2}(\sec \theta-\tan \theta)=$$\lim _{x \rightarrow \pi / 2}(\sec \theta-\tan \theta)= ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 If g(x)=2 x^{3}+\ln x is the derivative of f(x), find$$ \lim _{x \rightarrow 0} \frac{f(1+x)-f(1)}{x} $$0 answers 118 views If g(x)=2 x^{3}+\ln x is the derivative of f(x), find$$ \lim _{x \rightarrow 0} \frac{f(1+x)-f(1)}{x} $$If g(x)=2 x^{3}+\ln x is the derivative of f(x), find$$ \lim _{x \rightarrow 0} \frac{f(1+x)-f(1)}{x} $$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Evaluate \lim _{x \rightarrow 1}\left(\frac{y-4 \sqrt{y}+3}{y^{2}-1}\right) 1 answer 212 views Evaluate \lim _{x \rightarrow 1}\left(\frac{y-4 \sqrt{y}+3}{y^{2}-1}\right)Evaluate \lim _{x \rightarrow 1}\left(\frac{y-4 \sqrt{y}+3}{y^{2}-1}\right) ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 What do mathematicians mean by \lim _{x \rightarrow a} f(x)=\mathbf{L} 1 answer 82 views What do mathematicians mean by \lim _{x \rightarrow a} f(x)=\mathbf{L}What do mathematicians mean by \lim _{x \rightarrow a} f(x)=\mathbf{L} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Evaluate \lim _{x \rightarrow 10} f(x), where f(x)=x^{2} for all x \neq 10, but f(10)=99 . 0 answers 163 views Evaluate \lim _{x \rightarrow 10} f(x), where f(x)=x^{2} for all x \neq 10, but f(10)=99 .Evaluate \lim _{x \rightarrow 10} f(x), where f(x)=x^{2} for all x \neq 10, but f(10)=99 . ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Evaluate \lim _{x \rightarrow 10} \sqrt{-x^{2}+20 x-100} 1 answer 161 views Evaluate \lim _{x \rightarrow 10} \sqrt{-x^{2}+20 x-100}Evaluate \lim _{x \rightarrow 10} \sqrt{-x^{2}+20 x-100} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the limit \lim _{x \rightarrow-\infty} \frac{x-9}{2 x-x^{2}} 1 answer 116 views Find the limit \lim _{x \rightarrow-\infty} \frac{x-9}{2 x-x^{2}}Find the limit \lim _{x \rightarrow-\infty} \dfrac{x-9}{2 x-x^{2}} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Evaluate \lim _{x \rightarrow 10} \frac{x^{2}-100}{x-9} 1 answer 269 views Evaluate \lim _{x \rightarrow 10} \frac{x^{2}-100}{x-9}Evaluate \lim _{x \rightarrow 10} \frac{x^{2}-100}{x-9} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Determine \lim_{x \rightarrow 9}\dfrac{x^2-81}{\sqrt{x}-3} 1 answer 649 views Determine \lim_{x \rightarrow 9}\dfrac{x^2-81}{\sqrt{x}-3}Determine \lim_{x \rightarrow 9}\dfrac{x^2-81}{\sqrt{x}-3} ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find$$ \lim _{x \rightarrow 0} \frac{\sqrt{1+x}+(1+x)^{7}-2}{x} . $$1 answer 118 views Find$$ \lim _{x \rightarrow 0} \frac{\sqrt{1+x}+(1+x)^{7}-2}{x} . $$Find$$ \lim _{x \rightarrow 0} \frac{\sqrt{1+x}+(1+x)^{7}-2}{x} .$$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the limit$\lim _{x \rightarrow \infty} \frac{3 x+1}{|x|+2}$1 answer 146 views Find the limit$\lim _{x \rightarrow \infty} \frac{3 x+1}{|x|+2}$Find the limit$\lim _{x \rightarrow \infty} \dfrac{3 x+1}{|x|+2}$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the limit$\lim _{x \rightarrow \infty} \frac{6 x^{2}-4 x^{5}+7 x-1}{12 x^{5}-3 x^{2}+2}$1 answer 89 views Find the limit$\lim _{x \rightarrow \infty} \frac{6 x^{2}-4 x^{5}+7 x-1}{12 x^{5}-3 x^{2}+2}$Find the limit$\lim _{x \rightarrow \infty} \dfrac{6 x^{2}-4 x^{5}+7 x-1}{12 x^{5}-3 x^{2}+2}$... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Find the limit$\lim _{x \rightarrow \infty} \frac{x^{3}-6 x+1}{x^{2}+2 x-3}$1 answer 95 views Find the limit$\lim _{x \rightarrow \infty} \frac{x^{3}-6 x+1}{x^{2}+2 x-3}$Find the limit$\lim _{x \rightarrow \infty} \dfrac{x^{3}-6 x+1}{x^{2}+2 x-3}\$ ...