# Calc BC AP Test Review

 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) 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.) 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) 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 Outer radius - smaller radius 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) 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 What is... d/dx (au) = d/dx (au) = au ln(a) u' What is... d/dx log(u)= d/dx log(u)= 1/(u lna) * u' What is Rolle's Therom? Rolle's Therom: if f is continuous [a,b] and differentiable (a,b), and f(a)=f(b)=0then there is a number c that exists in (a,b) such that f'(c)=0 *rel. mins and maxs 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 General Procedure for Related Rates Problems!! 1.Read problem, draw diagram2.Variables and Math symbols for given info3. Write and equation involving the rate of change to be determined(reduced to one variable)4.Differentiate with respect to time5.Plug in values and solve for desired rate6.Answer with units of measure General Procedure for Solving Applied Max and Min Problems! 1. Write Primary Equation and Secondary Equation2. Solve so Primary Equation is in terms of one variable3. Find feasable domain4. Find critical values (f' = 0) of the function on the feasable domain5. Test critical numbers and endpoints6. Answer in context of the problem What is the Average Value of a Function? from (a,b) Average Value of a Function: 1/(b-a) ʃab f(x)dx Area of an equilateral triangle A= A=(s2 31/2) / 4 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)| First Fundamental Theorem of Calculus ʃab f(x)dx = F(b) - F(a) Second Fundamental Theorem of Calculus F(x)= ʃab f(t)= f(x) , F'(x)=f(x) at every point of [a,b] Area between two curves f(x) and g(x) ʃab [f(x)-g(x)]dxupper curve - lower curve 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) 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>1Series diverges when 0