Summary
Summary Mat135 Review Notes (calculus)
- Course
- Institution
- Book
Calculus review notes with key points and examples to help ace exam
[Show more]
Connected book
Book Title:
Author(s):
- Edition:
- ISBN:
- Edition:
More summaries for
-
"Key Concepts in Calculus"
-
Summary on Differentiation Rules-Calculus A (MAT1512)
-
Cheatengine Calculus 2
Seller
Follow
cookixxmonster
Content preview
MAT135 EXAM REVIEW NOTESTOPICS
❏ Calculate Limits
❏ Infinite Limits
❏ Limits to ∞
❏ Limit Laws
❏ Squeeze Theorem
❏ Continuity
❏ Intermediate Value Theorem
❏ Tangent Line of Function
❏ Derivative Rules
❏ Differentiability
❏ Implicit Differentiation
❏ Derivative of Inverse Trigonometry
❏ Exponential Growth/Decay
❏ Related Rate
❏ Critical Points
❏ Mean Value Theorem
❏ First Derivative Test
❏ Second Derivative Test
❏ L’Hopital’s Rule
❏ Optimization
❏ Limits of Arc Trigs
❏ Rolle’s Theorem
, How to Calculate Limits
Limit - the y-value a function approaches when it approaches an x-value
f (x+h) − f (x)
Official def’n of a derivative : l lim h
h→ 0
One-Sided Limits: Only looking at one side in question
Right-Handed Limit: lim f(x) = L
x→ a+
Left-Handed Limit: lim f(x) = L
x→a−
FACT
The limit lim x→ a f(x) = L will exist iff both the right and left handed limits are equal
Limit Properties
1. Constant Rule lim[cf(x)] = c limf(x)
2. Sum or Difference lim[f(x) +- g(x)] = lim f(x) +- lim g(x)
3. Product rule lim[f(x)g(x)] = limf(x)limg(x)
f (x) limf (x)
4. Quotient rule lim [ g(x) ] = limg(x) if limg(x) =/ 0
5. Power rule lim[f(x)]n = [limf(x)]n
6. Special Power rule lim n √f (x) = √ n
limf (x)
7. Limit of a constant is the constant limc = c
8. lim x→ a = a
9. lim x→ a xn = an
Ex: Compute lim as x→ -2 (3x2+5x -9)
1. lim 3x2 + lim5x - lim9
2. 3limx2 + 5limx - lim9
3. 3(-2)2+5(-2) -9 = -7
When can You just Plug in values?
- Polynomials
- p(x) / q(x) if no division of zero
- cos(x) and sin(x)
- sec(x) and tan(x), where cos(x) =/ 0
- csc(x) and cot(x), where sin(x) =/ 0
n
- √x if n is odd
- ax and ex
- logbx and lnx for all x > 0
ex
Ex : Evaluate lim (- √5 x + 1+ln(x) +sin(x)cos(x))
x→ 3
-this is just a combination of the several functions above, so we can just plug in the value
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller cookixxmonster. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $8.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
53022 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now