Question

Calculus.

Answer 1

@freckles @mathmath333

Answer 2

which letter are you asking for help with

Answer 3

All of them if I get a and b i should be able to do c and d

Answer 4

2.) natural logarithm

Answer 5

I'm not sure what definition for e is being asked about in number 1
is this not known in class?

Answer 6

maybe it wants us to use
\[\ln(x)=\int\limits_1^x \frac{1}{t} dt \\ \text{ and replace } x \text{ with } e^{e}\]

Answer 7

I think so maybe....

Answer 8

if so how would c and d work out?

Answer 9

\[\ln(e^e)=e \ln(e)=e(1)=e \\ e=\int\limits_1^{e^e} \frac{1}{t} dt\]

Answer 10

but I have no idea if that is what they are going for in number 1

Answer 11

perhaps it wants you to use it the other way
you know ln(e)=1
so replace my above x in the definition for ln(x) with e

Answer 12

so replace what from the first equation to figure out C?

Answer 13

I was saying what you should do probably for number 1

Answer 14

oh ok. I googled that and the same equation you put came up.

Answer 15

\[ \\ \text{ we want to show } e>2\]
so I would assume you would want to approximate ln(2) using the a finite amount of rectangles

Answer 16

ok so how do I do that?

Answer 17

take maybe like 4 rectangles on the given interval which is 1 to 2

Answer 18

I'm confused...

Answer 19

do you remember the integral definition of ln(x)?

Answer 20

\[\ln(x)=\int\limits_1^x \frac{1}{t} dt\]

Answer 21

we are using this to approximate ln(2)

Answer 22

\[\ln(2)=\int\limits_1^2 \frac{1}{t} dt \approx \text{... use one of those rules you learned to approximate the integral }\]

Answer 23

like midpoint rule or left endpoint rule or right end point rule

Answer 24

I would probably use both left endpoint and right endpoint rule

Answer 25

pretend you want 4 rectangles...
what would be the base length of each rectangle?