Facts Assessment Flashcards
Calc
∫ x^n dx
(x^( n+1 )) / (n+1) + c, where n ≠ 1
∫ 1 / (x^n) dx
(x^(-n+1)) / (-n+1) + c, where n ≠ 1
∫ 1 / x dx
lnlxl + c
∫ e^x dx
e^x + c
∫ a^x dx
(a^x) / lna + c
∫ sinx dx
-cosx + c
∫ cosx dx
sinx + c
∫ sec^2 x dx
tanx + c
∫ secxtanx dx
secx + c
∫ cscxcotx dx
-cscx + c
∫ csc^2 x dx
-cotx + c
What is the slope formula for parametric curves?
dy/dx = (dy/dt)/(dx/dt)
What is the formula for the 2nd derivative, d^2y/dx^2, for a parametric curve?
((dx/dt)(d^2y/dx^2)-(dy/dt)(d^2x/dt^2))/(dx/dt)^3
What is the arc length for a function, y=f(x)?
∫b/a √(1 + (dy/dx)^2)dx
What is the arc length formula for a parametric curve?
∫b/a √((dx/dt)^2 + (dy/dt)^2)dt
When does the speed of an object increase?
When velocity and acceleration have the same sign
When does the speed of an object decrease?
When velocity and acceleration have different signs
When does a particle change directions?
When its velocity changes signs
When is a particle at rest?
when velocity = 0
What formula is used to calculate the magnitude of a vector?
√(x^2 + y^2)
What formula is used to calculate the direction, θ, of a vector?
θ = tan^-1(y/x)
How is the speed of a velocity vector calculated?
√(f’(t)^2 + g’(t)^2)
What is the formula for calculating the total distance travelled for a vectorized curve?
∫b/a √(f’(t)^2 + g’(t)^2) dt
What is the formula for a velocity vector?
< dx/dt, dy/dt >
What is the formula for an acceleration vector?
< d^2x/dt^2, d^2y/dt^2 >
