Answer Limit Question: -3 | Good Day

[Mathnewbie]

Good Day

I have this limit question that I need to evaluate. I know the answer but am unsure how to answer it.

Evalualte:

lim (3^(x+1))(2-3^(-x))
x-> -Infinity

I know the answer is -3.

Any help would be great

 

[andrewchang]

have you tried it?

 

[andrewchang]

try distrubuting the $3^{x+1}$

 

[Mathnewbie]

just looking the my proofs solution I don't understand how 3^(x+1) * 2 = 2e^(x+1). Can anybody explain this?

 

[shmoe]

just looking the my proofs solution I don't understand how 3^(x+1) * 2 = 2e^(x+1). Can anybody explain this?

No, because they aren't equal.

 

[andrewchang]

i'm not sure what that is, but this is how i proved it:
$$\lim_{x\rightarrow -\infty} 3^{x+1} (2-3^{-x})$$
$$\lim_{x\rightarrow -\infty} 2(3^{x+1}) - 3^{x+1-x}$$
$$\lim_{x\rightarrow -\infty} 2(3^{x+1}) - 3$$
where x approaches negative infinity, therefore, $3^{-\infty} \rightarrow 0$
$$\lim_{x\rightarrow -\infty}3^{x+1} (2-3^{-x}) = - 3$$