Transcendental Numbers...5

What role does the number e play in Calculus l, ll, lll?

Same question for pi in terms of Calculus l, ll, lll.

This is it for today.

 

both play huge role

Whoever have taken an entry level calculus course, should have probably run into Euler’s constant, since it’s the base for the natural logarithms.
It looks like this: e^(ln( x))= x

e is the base of the natural logarithm, so it will be used constantly
Archimedes' π is defined as “the ratio of the circumference of a circle to its diameter.”

 

Going back to e^(ln x) = x, if x = 50, then we can say that e^(ln 50) = 50. Yes?

 

yes

 

This is cool.

Look: e^(ln Math) = Math.