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Find the exact value of the following limit: lim x approaches 0 e^6x... check photo above.​

Find the exact value of the following limit: lim x approaches 0 e^6x... check photo-example-1
User Trudbert
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Substituting x = 0 directly gives the indeterminate form 0/0, so you can use l'Hopital's rule (and you'll have to do that twice):


\displaystyle\lim_(x\to0)(e^(6x)-6x-1)/(x^2)=\lim_(x\to0)(6e^(6x)-6)/(2x)=\lim_(x\to0)\frac{36e^(6x)}2

The limand is continuous everywhere, so you can plug in x = 0 to get 36•1/2 = 18.

User Gabriel Esteban
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