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Question Number 91624 by john santu last updated on 02/May/20

Commented by john santu last updated on 02/May/20

$$whattheanswer?$$

Commented by arcana last updated on 02/May/20

$$f{}^{\prime }\left(0\right)=\underset{h\to 0}{\lim }\frac{f\left(h\right)-f\left(0\right)}{h}$$$$\Rightarrow f{}^{\prime }\left(0\right)\approx \frac{f\left(h\right)-f\left(0\right)}{h}$$$${hke}^{k0}\approx f\left(h\right)-1$$$$$$$$f\left(h\right)\approx 1+hk$$

Commented by mathmax by abdo last updated on 02/May/20

$$f\left(h\right)\sim f^{{}^{\prime }}\left(0\right)h+f\left(0\right)wehavef\left(x\right)=e^{kx}\Rightarrow f^{{}^{\prime }}\left(x\right)={ke}^{kx}\Rightarrow$$$$f^{{}^{\prime }}\left(0\right)=kalsof\left(0\right)=1\Rightarrow f\left(h\right)\sim kh+1$$$$correctanswerisD$$

Commented by john santu last updated on 02/May/20

$$yes.igotsameresult$$

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