Tardigrade
Question
Mathematics
An operator Δ is defined to operate on differentiable functions defined as follows. If f( x ) is a differentiable function then Δ(f( x ))= displaystyle lim h arrow 0 (f3( x + h )-f3( x )/ h ) g ( x ) is a differentiable function such that the slope of the tangent to the curve y = g ( x ) at any point (a, g ( a ) ) is equal to 2 e a ( a +1) also g (0)=0. displaystyle lim x arrow 0 (Δ g(x)/ ln ( cos 2 x))

Q. An operator $Δ$ is defined to operate on differentiable functions defined as follows. If $f (x)$ is a differentiable function then $Δ (f (x)) = h \to 0 lim \frac{f ^{3} ( x + h ) - f ^{3} ( x )}{h}$ $g (x)$ is a differentiable function such that the slope of the tangent to the curve $y = g (x)$ at any point (a, $g (a)$ ) is equal to $2 e^{a} (a + 1)$ also $g (0) = 0$ .
$x \to 0 lim \frac{Δ g ( x )}{ln ( cos 2 x )}$

92 166 Continuity and Differentiability Report Error

A

$- 12$

B

12

C

24

D

$- 24$

Solution:

Correct answer is (a) $- 12$