If f(4)=g(4)=2 ; f prime(4)=9 ; g prime(4)=6 then undersetx arrow 4 textLimit (√f(x)-√g(x)/√x-2) is equal to -

Question

If f(4)=g(4)=2 ; f prime(4)=9 ; g prime(4)=6 then undersetx arrow 4 textLimit (√f(x)-√g(x)/√x-2) is equal to - (A) 3 √2 (B) (3/√2) (C) 0 (D) none of these

Tardigrade Admin · Accepted Answer

displaystyle lim x arrow 4 (√f(x)-√g(x)/√x-2)= displaystyle lim x arrow 4 ((1/2) (f prime(x)/√f(x))-(1/2) (g prime(x)/√g(x))/(1)2 √x) =((9/√2)-(6/√2)/(1)2)=3 √2

Q. If $f (4) = g (4) = 2; f^{'} (4) = 9; g^{'} (4) = 6$ then $x \to 4 Limit \frac{f ( x ) - g ( x )}{x - 2}$ is equal to -

$32$

$\frac{3}{2}$

0

none of these

$x \to 4 lim \frac{f ( x ) - g ( x )}{x - 2} = x \to 4 lim \frac{\frac{1}{2} \frac{f ^{'} ( x )}{f ( x )} - \frac{1}{2} \frac{g ^{'} ( x )}{g ( x )}}{\frac{1}{2 x}}$
$= \frac{\frac{9}{2} - \frac{6}{2}}{\frac{1}{2}} = 32$

Q. If f(4)=g(4)=2;f′(4)=9;g′(4)=6 then x→4Limit​x​−2f(x)​−g(x)​​ is equal to -

32​

2​3​

0

none of these

x→4lim​x​−2f(x)​−g(x)​​=x→4lim​2x​1​21​f(x)​f′(x)​−21​g(x)​g′(x)​​ =21​2​9​−2​6​​=32​

Q. If $f (4) = g (4) = 2; f^{'} (4) = 9; g^{'} (4) = 6$ then $x \to 4 Limit \frac{f ( x ) - g ( x )}{x - 2}$ is equal to -

$32$

$\frac{3}{2}$

$x \to 4 lim \frac{f ( x ) - g ( x )}{x - 2} = x \to 4 lim \frac{\frac{1}{2} \frac{f ^{'} ( x )}{f ( x )} - \frac{1}{2} \frac{g ^{'} ( x )}{g ( x )}}{\frac{1}{2 x}}$
$= \frac{\frac{9}{2} - \frac{6}{2}}{\frac{1}{2}} = 32$