Let fx-gx-x when x-0 and f0-0- If g0-g10 and g110-17 then f10A- 3-4B- -1-2C- 17-3D- 17-2

The correct option is D f^1(0)=Ltx→0f(x) f(0)/x 0=Ltx→0f(x)/x =Ltx→0g(x)/x^2=Ltx→0g^11(x)/2=g^11(0)/2=17/2 ...

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Byju's Answer

Standard XII

Mathematics

Arithmetic Progression

Let fx=gx/x w...

Question

$L e t f (x) = \frac{g (x)}{x} w h e n x \neq 0 a n d f (0) = 0 . I f g (0) = g^{1} (0) a n d g^{11} (0) = 17 t h e n f^{1} (0)$

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Solution

The correct option is D
$f^{1} (0) = L t x \to 0 \frac{f (x) - f (0)}{x - 0} = L t x \to 0 \frac{f (x)}{x} = L t x \to 0 \frac{g (x)}{x^{2}} = L t x \to 0 \frac{g^{11} (x)}{2} = \frac{g^{11} (0)}{2} = \frac{17}{2}$

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Let f(x)=g(x)x when x≠0 and f(0)=0. If g(0)=g1(0) and g11(0)=17 then f1(0)

The correct option is D f1(0)=Ltx→0f(x)−f(0)x−0=Ltx→0f(x)x=Ltx→0g(x)x2=Ltx→0g11(x)2=g11(0)2=172

$L e t f (x) = \frac{g (x)}{x} w h e n x \neq 0 a n d f (0) = 0 . I f g (0) = g^{1} (0) a n d g^{11} (0) = 17 t h e n f^{1} (0)$

The correct option is D
$f^{1} (0) = L t x \to 0 \frac{f (x) - f (0)}{x - 0} = L t x \to 0 \frac{f (x)}{x} = L t x \to 0 \frac{g (x)}{x^{2}} = L t x \to 0 \frac{g^{11} (x)}{2} = \frac{g^{11} (0)}{2} = \frac{17}{2}$