E Infinity Limit
And for the second limit after applying. If a is nonpositive as you can see the limit will be 0.
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Te xplanation of why will depand a great deal on the definitions of ex and lnx with which you are working.
E infinity limit. The limit does not exist because as x increases without bond ex also increases without bound. I like to define lnx int_1x 1t dt for x 0 then prove that lnx is invertible has an inverse and define e. For the first limit itll have to depend on what the value of a is.
The first is clearly infinity and the second is clearly a finite number one in this case and so the Facts from the Infinite Limits section gives us the following limit lim x e 10 x 4 e 6 x 3 e x 2 e 2 x 9 e 15 x lim x e 10 x 4 e 6 x 3 e x 2 e 2 x 9 e.
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