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Question Number 27696 by chernoaguero@gmail.com last updated on 12/Jan/18

$$$$$$$$$$\underset{x\to 0}{\lim }\frac{{\mathrm{ae}}^{\mathrm{x}}+{3\mathrm{e}}^{2\mathrm{x}}-\mathrm{b}}{\mathrm{x}}=8$$$$$$$$\mathrm{find}\mathrm{a}\mathrm{and}\mathrm{b}$$

Commented by abdo imad last updated on 12/Jan/18

$$\iff {lim}_{x->0}\frac{a{e}^x+3e^{2x}-8x-b}{x}=0a+3-b=0a-b=-3$$$${lim}_{x->0}a{e}^x+6e^x-8=0\Rightarrow a+6-8=0\Rightarrow a=2\Rightarrow -b=-5\Rightarrow b=5$$$${lim}_{x->0}\frac{2e^x+3e^{2x}-5}{x}={lim}_{x->0}2e^x+6e^{2x}=8so$$$$a=2andb=5\left(wehaveusedhospitaltherem\right)$$

Commented by chernoaguero@gmail.com last updated on 12/Jan/18

$$\mathrm{ok}\mathrm{thank}\mathrm{u}\mathrm{sir}$$

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