Introducing 

Prezi AI.

Your new presentation assistant.

Refine, enhance, and tailor your content, source relevant images, and edit visuals quicker than ever before.

Loading content…
Loading…
Transcript

L' Hopitals Rule

Conceptual Knowledge

If there is a point x=a, where f(x) and g(x) intersect, then you can take the limit as x approaches "a" of f(x) and g(x) separately. The ratio of the 2 instantaneous rate of changes at x=a will be the limit as the orginal function f(x) / g(x) approaches "a".

Find the Limit

(1/x)

lim X

x->∞

Indeterminate Form

Formula

Indeterminate form is a ratio that you get when you use substitution to solve the limit.

When you substitute, you get a ratio that does not give you a real answer.

This is where L' Hopital's rule comes in handy.

IF

Lim f(x)=Lim g(x)=0 or (+/-)∞

X->C

Find "m" so f(x) is cont.

Work Book Page 30, #12

Background

exists and g'(x) ≠ 0

and Lim f’(x)

___

cos(2x)-1 , x≠0

{

f(x)=

m , x=0

g'(x)

X->C

Then Lim f(x) = Lim f'(x)

___

  • Helps us deal with complicated limits that we cant solve with prior tools such as sub. and algebra.
  • Uses differentiation to solve these limits that are in indeterminate forms

g'(x)

g(x)

X->C

More Indet form

Find the Limit

1

____

(+/-) ∞ - (+/-) ∞

If we get this as our ratio when subbing, we would use algebra to get it into the proper indet form.

1∞

If we get this, then we would take the natural log which would bring down the exponent. Then we use algebra to get intot the proper indet form if its not already in it.

Lim

-

( )

ln(x)

(x-1)

X->1

Types of Forms

  • 0/0 - regular l' hopitals rule
  • (-)∞/(-)∞ - regular l' hopitals rule
  • A/0 - If this ratio happens, depending on whether the func approaches from left or right, limit will be pos ∞ or neg ∞
  • 0/A - If this ratio comes up then the limit as the function approaches the limiting value would be 0.
Learn more about creating dynamic, engaging presentations with Prezi