# Calc BC AP Test Review

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1. Volume of a Solid with Cross Section

V=
Volume of a Solid with Cross Section

• V=ʃab A(x)dx
• (cross section is perp. to height of solid)
2. Euler's Method when y'=F(x,y)

x1=
y1=
Euler's Method when y'=F(x,y)

• x1= x0+h y1= y0+hF(x0,y0)
• h is step size
• (smaller step size, better approx.)
3. Disc Method about the line h

V=
Disc Method about the line h

• V= (pi) ʃab( f(x) - h )2 dx,
• where | f(x)-h |=radius
• (if x-axis, h=0)
4. Washer Method between f(x) and g(x)

V=
Washer Method between f(x) and g(x)

• V=(pi) ʃab [ (f(x))2 - (g(x))2 ]dx
5. What is the Squeeze Therom?
if g(x)< f(x) < h(x) and Limx->a[g(x)= h(x)]=L, then so does that same limit of f(x)
6. What is the Intermediate Value Therom?
If a function f is continuous on a closed interval [a,b] and k is a number with f(a) < k < f(b), there exists a number inside the interval where f(c)=k
7. What is...

d/dx (au) =
d/dx (au) = au ln(a) u'
8. What is...

d/dx log(u)=
d/dx log(u)= 1/(u lna) * u'
9. What is Rolle's Therom?
• Rolle's Therom: if f is continuous [a,b] and differentiable (a,b), and f(a)=f(b)=0
• then there is a number c that exists in (a,b) such that f'(c)=0
• *rel. mins and maxs
10. What is the Mean Value Therom?
• Mean Value Therom: if f is continuous [a,b] and differentiable (a,b) thn there exists a number c in (a,b) that f'(c)=(f(b)-f(a))/(b-a)
• *secant line slope passing through points a and b are equal to tangent slope of c
11. General Procedure for Related Rates Problems!!
• 1.Read problem, draw diagram
• 2.Variables and Math symbols for given info
• 3. Write and equation involving the rate of change to be determined(reduced to one variable)
• 4.Differentiate with respect to time
• 5.Plug in values and solve for desired rate
• 6.Answer with units of measure
12. General Procedure for Solving Applied Max and Min Problems!
• 1. Write Primary Equation and Secondary Equation
• 2. Solve so Primary Equation is in terms of one variable
• 3. Find feasable domain
• 4. Find critical values (f' = 0) of the function on the feasable domain
• 5. Test critical numbers and endpoints
• 6. Answer in context of the problem
13. What is the Average Value of a Function? from (a,b)
Average Value of a Function: 1/(b-a) ʃab f(x)dx
14. Area of an equilateral triangle

A=
A=(s2 31/2) / 4
15. Position Function
Instantaneous Velocity
Acceleration
Instantaneous Speed
• Position Function = s(t)
• Instantaneous Velocity = s'(t) = v(t)
• Acceleration = s''(t) = v'(t) = a(t)
• Instantaneous Speed = |v(t)|
16. First Fundamental Theorem of Calculus
ʃab f(x)dx = F(b) - F(a)
17. Second Fundamental Theorem of Calculus
F(x)= ʃab f(t)= f(x) , F'(x)=f(x) at every point of [a,b]
18. Area between two curves f(x) and g(x)
• ʃab [f(x)-g(x)]dx
• upper curve - lower curve
19. Distance Trveled Problems!!

Displacement from t1 to t2
• Displacement from t1 to t2 = ʃt1t2 v(t)
• Total distance traveled is the same thing but the absolute value of v(t)
20. p-series
• is a series of the form, 1+1/2p=1/3p=1/4p+...+1/np+...= sum( 1/np, n, 1, infinity)
• Series converges when p>1
• Series diverges when 0<p<1
21. harmonic series
special p series, where p=1, so the series diverges
22. geometric series
• sum(ar(n),n,0,infinity).
• series converges when |r|<1
• sum of the series is a/(1-r)
23. integral test
if an=f(n) where f is continuous, positive, decreasing funciton on [c,infinity)

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 Author: meghanking ID: 82042 Filename: Calc BC AP Test Review Updated: 2011-04-27 01:33:37 Tags: calc Folders: Description: calc Show Answers:

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