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

1. ## 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)

2. 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 $f(x)=\begin{cases} x^3+1 & \mbox{if}\quad x<1 \\ 1+\frac{1}{x} & \mbox{if}\quad x\geqslant 1\end{cases}$

For the limits, clearly $\lim_{x\to\infty}f(x)=1$, right? Also, $\lim_{x\to-\infty}f(x)=-\infty$.

3. 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?

4. 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 $\delta-\varepsilon$.