Exam (elaborations)
Calculus II final review Questions and Answers
- Course
- Institution
Calculus II final review Questions and Answers Sinh(x) *** (e^x-e^-x)/2 Cosh(x) *** (e^x+e^-x)/2 How do you eliminate the parameter? *** Solve for t
[Show more]
Seller
Follow
smartchoices
Reviews received
Content preview
Calculus II final review Questions and AnswersSinh(x) *** (e^x-e^-x)/2
Cosh(x) *** (e^x+e^-x)/2
How do you eliminate the parameter? *** Solve for t
Pythagorean Identity *** cos^2x+sin^2x=1
Speed *** √(dx/dt)^2+(dy/dt)^2
Acceleration *** √(d^2x/dt^2)^2+(d^2y/dt^2)^2
Second derivative on a parametric curve *** (d/dt * dy/dx)/(dx/dt)
Integration by parts *** ∫ u dv = uv - ∫ v du
L.I.A.T.E *** logarithmic, inverse trig, algebraic, trig, exponential
Partial Fractions *** An/(x-an)...
√a^2-x^2 *** x=asin(theta)
a^2+x^2 *** x=atan(theta)
Right sum *** Delta x * Σ from j=1 to N f(a+j* Delta x)
Left sum *** Delta x * Σ from j=0 to N-1 f(a+j* Delta x)
Trapezoidal Sum *** Delta x [(f(x0)+f(xN))/2] + Σ from j=1 to N-1 of
f(a+j*delta x) OR 1/2(Right sum + Left Sum)
Midpoint/Tangent sum *** Delta X Σ from J=1 to N of f(a+(j-1/2)Delta x)
, Simpson's rule *** Trap sum/3 + 2*Mid Sum/3
Simpson's rule (Without using the sums) *** 1/3*delta x[y0+4y1+2y2 ... + 4yn-
1+yn] (Starts by adding the first Y and then alternates with 2 &4 but N-1 must
always end with 4)
Error bound for Simpson's rule *** [Ksub4*(b-a)^5]/180* N^4 where K sub 4 =
the max value at the fourth derivative of the function within the given interval
P integral for improper integrals *** if P is <=1 Diverges if P is > 1 converges to
(a^(1-p)/p-1)
Integral comparison test comparing f(x) to g(x) *** if g(x)> f(x) and g(x)
converges f(x) converges
if g(x)< f(x) and g(x) diverges f(x) diverges
if g(x)> f(x) and g(x) diverges f(x) is unknown (try again)
if g(x)< f(x) and g(x) converges f(x) is unknown (try again)
Finding volume of Revolution using Disk method *** ∫ from a to b of π*[f(x)]^2
dx. Use when rotation creates a disk who's radius r =f(x ) so that the integral is just
πr^2dx
Finding volume of Revolution using Washer method *** ∫ from a to b of
π[(R(x))^2-(r(x))^2]dx. Use when rotation creates 2 disks or a "hole" and then
subtract big R from little r
Finding volume or Revolution using Cylindrical Shell method *** ∫ from a to b
of 2πx*f(x) dx. When rotated around the y axis and bounded by x
Arc Length over [a,b] *** ∫ from a to b √1+[f'(x)]^2 dx
Area of a Surface of Revolution *** 2 π ∫ f(x) √1+[f'(x)]^2 dx
Arc Length of a Parametric curve *** ∫ √x'(t)^2+y'(t)^2 dt from a to b
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 smartchoices. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $8.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
83637 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now