1. Tardigrade
  2. Question
  3. Mathematics
  4. 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))

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Q. An operator $\Delta$ is defined to operate on differentiable functions defined as follows. If $f( x )$ is a differentiable function then $\Delta(f( x ))=\displaystyle\lim _{ h \rightarrow 0} \frac{f^3( x + h )-f^3( x )}{ h }$ $g ( x )$ 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 $g (0)=0$.
$\displaystyle\lim _{x \rightarrow 0} \frac{\Delta g(x)}{\ln (\cos 2 x)}$

Continuity and Differentiability

Solution:

Correct answer is (a) $-12$