Question

Calc 1 question?

Answer 1

I am so confused.... @welshfella
@freckles

Answer 2

are they looking for int from 0 to e dx? for a?

Answer 3

I know b is natural log.

Answer 4

thats correct for b

Answer 5

http://mathworld.wolfram.com/e.html

Answer 6

for a yesterday we concluded that we are using ln(x) 's definition
\[\ln(x)=\int\limits_1^x \frac{1}{t} dt \]
we replace x with e
\[\ln(e)=\int\limits_1^e \frac{1}{t} dt=1\]

which is actually in @robtobey 's website thingy above

Answer 7

Right I was taking with zep and he said he couldnt figure out how to apply that to c and d

Answer 8

we want to approximate ln(2) and ln(3) using something like right endpoint rule

Answer 9

ok so how do we do that? is it like the rectangles under a curve thing?

Answer 10

yes

Answer 11

except this will be an overestimation

Answer 12

ok so how do I set it up?

Answer 13

part d says use 1/4 as the measurement for the base length of each rectangle

Answer 14

you know a=1 and b=3 since \[\ln(3)=\int_1^3 \frac{1}{t} dt\]

Answer 15

so if we want base length 1/4 and we have a=1 and b=3
then how do you figure out the number of rectangles the hint is suggesting to use?

Answer 16

hint: use the formula for Delta x

Answer 17

well if it has to be under 3 it should be 12 ?

Answer 18

\[\Delta x=\frac{b-a}{n}\]
you know this right?

Answer 19

we are given Delta x=1/4

Answer 20

\[\frac{1}{4}=\frac{3-1}{n}\]

Answer 21

n is the number of rectangles

Answer 22

so 8

Answer 23

1/4=2/8

Answer 24

yes we will need 8 rectangles for d

Answer 25

so you will find 8 heights since we have 8 rectangles
the heights can be found by using f and the right endpoint of each sub-interval

Answer 26

for the example the first subinterval is
[1,1+1/4]=[1,5/4]
the second subinterval is
[5/4,5/4+1/4]=[5/4,6/4]
continue this until you have gotten 3 is your right endpoint (or until you have 8 subintervals)