Exam (elaborations)
APMA 1110 Test Review questions with complete solutions
- Course
- Institution
APMA 1110 Test Review questions with complete solutions
[Show more]
Content preview
APMA 1110 Test ReviewIntegration by parts - correct answer ✔✔∫ u dv = uv - ∫ v du
derivatives of sin, cos, and tangent (and sec) functions (6) - correct answer ✔✔d/dx sinx=cosx
d/dx cosx=-sinx
d/dx tanx=sec2x
d/dx sinu= cosu*u'
d/dx cosu= -sin(u)*u
'd/dx tanu = sec2u*u'
d/dx secx= secxtanx
derivatives of sec^2, cot, and csc functions - correct answer ✔✔d/dx sec^2x=tanx
d/dx -cotx= -csc^2x
d/dx -cscx= -cscxcotx
Derivative Rule for Inverses (arcsin, arccos, arctan) - correct answer ✔✔d/dx arcsinx = 1/rad(1-x^2)
d/dx arccosx = -(1/rad(1-x^2) )
d/dx arctan = 1/(1+x^2)
derivative of e and ln (4) - correct answer ✔✔d/dx e^x = e^x
d/dx e^f(x) = e^f(x) * f'(x)
d/dx lnx= 1/x
d/dx ln(f(x))= 1/f(x) * f'(x)
Anti-power rule - correct answer ✔✔(cx^n+1)/n+1
, Anti-chain rule substitution.
What things do you make the u? - correct answer ✔✔Make the u:
- something raised to a power
- something inside a trig function
- power of e
- denominator of a fraction
if the x doesn't cancel out when you are using a u substitution, what do you do? - correct answer
✔✔Take original u substitution and solve for x and plug x = in what hasn't been crossed out. Multiply u's
together and solve.
Antiderivative trig functions - correct answer ✔✔anti derivative of cosx: sinx
anti derivative of sinx: -cosx
anti derivative of -sinx: -cosx
anti derivative of sec^2x: tanx
anti derivative of secxtanx: secx
anti derivative of csc^2x: -cotx
anti derivative of tan^2x: tanx-x
anti derivative of tanx: ln|secx|
Antiderivative of e's and 1/x - correct answer ✔✔anti derivative of e is e
anti derivative of 1/x is ln|x|
Antiderivative of ln - correct answer ✔✔xlnx-x
antideriv of inverse sin - correct answer ✔✔xsin^-1x-∫x/(sqrt(1-x^2)
Choosing u - correct answer ✔✔Inverse
Log
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 Sakayobako30. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $12.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
82191 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now