Question

Estimate the limit by substituting smaller and smaller values of h. Round the answer to one decimal place!! :)

lim (e^4+h) - (e^4)
h->0 --------------
h

so trying to sub 0.1,0.01,0.001, and 0.000001 (for more reference hehe)

do these look right?

h=0.1... 57.42137
h=0.01...54.87205
h=0.001...54.625458
h=0.000001...54.598176

so would it be approaching 54 point something? not sure if that's right so far though. what do you think @zepdrix ?? :)

Answer 1

h is in in the exponent position?

e^(4+h) ?

Answer 2

ya they look good!

Answer 3

yes:)

Answer 4

54 point something, 1 decimal again?

Answer 5

okay yay!! :)

but not sure what the decimal point would be :/


haha yeah, one decimal point:)

Answer 6

The expression represents the limit definition of the derivative of the function e^x evaluated at x=4.

The derivative of e^x is e^x.
Evaluated at x=4 gives us e^4.

So if you're having trouble figuring out exactly what value it's approaching, punch that into your calculator real quick.

I know I know, it's kinda cheating.. but it's good to see the connection with these things.

Answer 7

e^4=54.5981.....

so does that give us the answer then? hahaha :P

would it be 54.6 ?

Answer 8

It's approaching 54.5981...

So if you need to round to 1 decimal value, yah 54.6 is probably a good idea :O

Answer 9

hehe okie yay:) thanks!!....again!! haha :P