# Math Help - limits

1. ## limits

Hi there ! I really need these done by next friday. I tried to do my best to translate this to english from ICELANDIC and hopefully you'll all understand these consepts. If not, leave me a line and I'll do my best to answer you all.

1. a Are the following limits possible, and if so please find them. If not, argue:

1. a
lim $x^3+2x^2/-x^3+8$
x->infinity

1. b
lim $|2x-4/2x-4$
x->2

1. c
lim $3x+5/16x+8x+x^2$
x->-4

1. b Find the argument of these functions:
$f(x)=x^3+2x^2/-x^3+8$ and $g(x)=x^2+2x+4/2x$

1. c Find the limits:
lim $(e^x+1)$ and lim $(e^x+1)$
x->infinity x->-infinity

1. d Does the function $f(x)=e^x+1$ any arguments ?

2. a The function $f(x)=x^3-1/x^2-1$ is not conjoined in two specific points (x,y). Which points are they and why ?

2. b Can you find any answer for f(x) in these points noted before so the function becomes conjoined and if so, which points are they. And if not, how come ?

3. A mountain climber starts climbing a mountain at 10.00 am and reaches the top at 02.00 pm. He then spends the night at the top. The next morning he goes downhill at 10.00 am and is down at his car (at the very same spot he started) at 02.00 pm.
Is it possible that at some point on the first day he is in the exactly same altitude as the latter day and also at the same exact time ? Please argue.

- AG

2. Originally Posted by Arni
Hi there ! I really need these done by next friday. I tried to do my best to translate this to english from ICELANDIC and hopefully you'll all understand these consepts. If not, leave me a line and I'll do my best to answer you all.

1. a Are the following limits possible, and if so please find them. If not, argue:

1. a
lim $x^3+2x^2/-x^3+8$
x->infinity

1. b
lim $|2x-4/2x-4$
x->2

1. c
lim $3x+5/16x+8x+x^2$
x->-4
for 1. a and 1. c, i just addressed a problem a problem here that might help. see posts #8 and #10.

for 1. b, there seems to be a typo or something. what does that | in front of the 2 mean?

1. b Find the argument of these functions:
$f(x)=x^3+2x^2/-x^3+8$ and $g(x)=x^2+2x+4/2x$
what do you mean by the "argument" of the functions?

1. c Find the limits:
lim $(e^x+1)$ and lim $(e^x+1)$
x->infinity x->-infinity
hint: what does the function $e^x$ look like? when x gets large, what happens? does adding 1 change the function much?

another hint: negative powers mean we take the reciprocal of the function. so, for instance, $e^{-x} = \frac 1{e^x}$. use this as a hint for the limit as $x \to - \infty$

1. d Does the function $f(x)=e^x+1$ any arguments ?
still don't know what you mean here

2. a The function $f(x)=x^3-1/x^2-1$ is not conjoined in two specific points (x,y). Which points are they and why ?
hint: recall what a "hole" is

2. b Can you find any answer for f(x) in these points noted before so the function becomes conjoined and if so, which points are they. And if not, how come ?
did you find all the points where the function is discontinuous? did you find the vertical asymptotes and holes?

3. Here are some corrections.
1. b should've been:
$lim |2x-4|/2x-4$
x->2

And sorry last night I didn't quite get the ARGUMENT translation right. What I meant is asymptote.

Thanks for all your help, but even with all your hints, tips and tricks I can't solve these problems. I'm terribly bad at math I'm sorry. Is there any chance you can do these for me and argue why you do it ? It would help me learn so much.

- AG

4. 1. c Find the limits:
lim e^(x+1) and lim e^(x+1)
x->infinity x->-infinity

What happens when you raise any positive number (greater than 1) to 10? It gets bigger. What about raising it to 100? It gets even bigger. The higher the number you raise it to, the bigger the number will get. Eventually it will get so big that there's nothing to do but call it infinity.
(Example: 3^100,000,000,000,000. There's no way that we could actually come up with a numerical value for it without spending the rest of our lives trying to write it out. We just call it infinity.)

For the negative infinity, it's the same sort of thing. But what happens when you have a negative exponent? Then remember that 1/2 > 1/3 > 1/4 > 1/5, etc.

5. Originally Posted by Arni
Here are some corrections.
1. b should've been:
$lim |2x-4|/2x-4$
x->2
recall, $|x| = \left \{ \begin{array}{lr} x & \mbox{ if } x \ge 0 \\ & \\ -x & \mbox{ if } x < 0 \end{array} \right.$

so, $\frac {|2x - 4|}{2x - 4} = \left \{ \begin{array}{lr} \frac {2x - 4}{2x - 4} & \mbox{ if } 2x - 4 \ge 0 \\ & \\ - \frac {2x - 4}{2x - 4} & \mbox{ if } 2x - 4 < 0 \end{array} \right.$

now can you do it?

And sorry last night I didn't quite get the ARGUMENT translation right. What I meant is asymptote.
see post #2 here

Thanks for all your help, but even with all your hints, tips and tricks I can't solve these problems. I'm terribly bad at math I'm sorry. Is there any chance you can do these for me and argue why you do it ? It would help me learn so much.