# can someone check my work on this relaively easy limit problem

• Dec 17th 2009, 12:23 AM
twostep08
can someone check my work on this relaively easy limit problem
5. Find all the local and absolute extrema (maxima and minima) for
f
(x) = x^3 +1 for x<1
1/x + 1 for x greater than or equal to 1

also calculate the limits as x goes to + and - infinity

i got local max when x=1
i dont think there are any absolute extrema

and i think the lim as x goes to +infinity is 0
and as x goes to -ininity is positive infinity...how do i show thats the case?

am i right on all counts?

unfortunately ill be on here for the next 2-3 hours or so, so if you could help me with any of the questions ive yet asked id be extremely grateful (with my last and worst one still to come:()

• Dec 17th 2009, 12:32 AM
Drexel28
Quote:

Originally Posted by twostep08
5. Find all the local and absolute extrema (maxima and minima) for

f
(x) = x^3 +1 for x<1

1/x + 1 for x greater than or equal to 1

also calculate the limits as x goes to + and - infinity

i got local max when x=1
i dont think there are any absolute extrema

and i think the lim as x goes to +infinity is 0
and as x goes to -ininity is positive infinity...how do i show thats the case?

am i right on all counts?

unfortunately ill be on here for the next 2-3 hours or so, so if you could help me with any of the questions ive yet asked id be extremely grateful (with my last and worst one still to come:()

I believe your function is $\displaystyle f(x)=\begin{cases} x^3+1 & \mbox{if}\quad x<1 \\ 1+\frac{1}{x} & \mbox{if}\quad x\geqslant 1\end{cases}$

For the limits, clearly $\displaystyle \lim_{x\to\infty}f(x)=1$, right? Also, $\displaystyle \lim_{x\to-\infty}f(x)=-\infty$.
• Dec 17th 2009, 12:43 AM
twostep08
right you are...im gettin tired havent slept in a long time. are my mins/maxs right? and how should i show the limit approaches those?
• Dec 17th 2009, 12:49 AM
Drexel28
Quote:

Originally Posted by twostep08
right you are...im gettin tired havent slept in a long time. are my mins/maxs right? and how should i show the limit approaches those?

To be honest, I am not in a min-max mood right now :/. To show them you would have to do $\displaystyle \delta-\varepsilon$.