# Limits...numerically

• September 6th 2007, 02:53 PM
mer1988
Limits...numerically
Estimate the limit by substituting smaller and smaller values of h. Give your answer to three decimal places.

lim as h -> 0 for 3^h - 1 / h

much thanks
• September 6th 2007, 02:58 PM
ThePerfectHacker
Quote:

Originally Posted by mer1988
Estimate the limit by substituting smaller and smaller values of h. Give your answer to three decimal places.

lim as h -> 0 for 3^h - 1 / h

much thanks

$\lim_{h\to 0} \frac{3^h - 1}{h}$.

Let $h=1$ then $h=.1$ then $h=.01$ then $h=.001$. Substitute that in. What does it seem to be approaching?
• September 6th 2007, 03:09 PM
mer1988
its seems to be approaching 1.1
• September 6th 2007, 03:17 PM
ThePerfectHacker
If you want to be extra accurate it is 1.099
• September 6th 2007, 03:26 PM
mer1988
yeah, cuz it wanted it to three decimal places...thank you...

i have one more questoin, i got the first part but i need help with the other one...

t(sec) 0 0.2 0.4 0.6 0.8 1.0
s(ft) 0 0.1 1.4 3.4 6.2 9.6

the first part is 5.7ft/s the avg. velocity, then the second part asks, estimate the velocity of the car at t=0.6

then i dont know where to go
• September 6th 2007, 03:39 PM
Krizalid
That's a completely different question, give it its own thread.
• September 6th 2007, 03:43 PM
topsquark
Quote:

Originally Posted by mer1988
yeah, cuz it wanted it to three decimal places...thank you...

i have one more questoin, i got the first part but i need help with the other one...

t(sec) 0 0.2 0.4 0.6 0.8 1.0
s(ft) 0 0.1 1.4 3.4 6.2 9.6

the first part is 5.7ft/s the avg. velocity, then the second part asks, estimate the velocity of the car at t=0.6

then i dont know where to go

There are two ways to answer this depending on how much work you want to put into it. (I'd recommend the longer way.)

The long way: Plot your points using t as your x axis and s as your y axis. Sketch a smooth curve connecting the points. Now, at t = 0.6 s draw a line tangent to the curve. The slope of this line is your speed at t = 0.6 s.

The quick way: It may be that your teacher hasn't taught you about that yet. So what I would do is find the average speed of the car between t = 0.4 s and t = 0.6 s, then again do it between t = 0.6 s and t = 0.8 s. Hopefully these two will be close because I'm about to (statistically speaking) screw things up. Average the two average speeds that you got. Taking the average of two averages is technically forbidden unless the graph is a straight line, but you should get a rough value doing this. (Something you might wish to do is to compare this "average average" with the average speed between the times t = 0.4 s and t = 0.8 s.)

-Dan
• September 6th 2007, 03:49 PM
mer1988
thanks...that worked, i was just findin the average between .4 and .6 and using that, i didnt know that doing it between .4 and .8 works too..

thanks again