LIMITS

[italiangijoe]

Question 1:

f(x) = xe^-x

Find
a) limit f(x), x approaching zero
b) limit f(x), x approaching positive infinity
c) limit f(x), x approaching negative infinity

My answers:
a) 0
b) positive infinity
c) negative infinity

It seemed too easy. Like I shouldn't just be able to plug it in.

Second question:

lim e^4x - 1/ x^2 , x approaching positive infinity

I simplified it down to 8(e^4x), using L'Hospital Rule, and my answer was positive infinity. This one just seemed odd to me.

Third question:

lim (x^2 + x)^(1/2) - x
x->0

If you plug in zero, you get 0 - 0= 0. Again, it just seemed too easy.

Any suggestions?

 

[tkhunny]

Rethink 1.b Perhaps it would be beneficial to rewrite as \(\displaystyle \frac{x}{e^{x}}\).

 

[tkhunny]

For 2, please rewrite for clarity. Remember Order of Operations. It's important.

e^4x - 1/ x^2 means \(\displaystyle e^{4}\cdot x - \frac{1}{x^{2}}\) Is this what you intended?

Perhaps \(\displaystyle e^{4x} - \frac{1}{x^{2}}\)

Perhaps \(\displaystyle e^{4x-\frac{1}{x^{2}}}\)

Perhaps \(\displaystyle \frac{e^{4x}-1}{x^{2}}\)

It's an important concept to keep in your mind. "Never write what you don't mean." - TKHunny