Help: Derivative of Function

if $f(x)$ is a function such that $f\left( 0 \right) =a, f^{ ' }\left( 0 \right) =ab, f^{ '' }\left( 0 \right) =a{ b }^{ 2 }, f^{ ''' }\left( 0 \right) =a{ b }^{ 3 },$ and so on and $b>0$ , where dash denotes the derivatives, then compute $\displaystyle \lim _{ x\to -\infty }{ f\left( x \right) }$ .

#Calculus

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
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Comments

parv mor - 5 years, 4 months ago

Yes that is the answer. Now, if you could please post the solution.

Akhilesh Prasad - 5 years, 4 months ago

@parv mor, @Rishabh Cool, Please can you provide a solution.

Akhilesh Prasad - 5 years, 4 months ago

F(x) = ae^(bx) Expand by taylor series and you will understand

parv mor - 5 years, 4 months ago

Thnaks a lot mate

Akhilesh Prasad - 5 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$