Derivatives
(d/dx)(4x^2+8x+16)
What is 8x+8?
Int (1/x)dx
what is ln|x|+C?
Lim x to 2 ((x^2-4)/(x-2))
what is 4?
IVT
What is the Intermediate Value theorem?
If position is S(t), what is velocity?
What is S’(t)?
(d/dx)(1/x)
what is -1/x^2?
Int 0 to π (sin(x))dx
what is 2?
Lim x to 4 (3x^3+12x^2-8x+36)
what is 388?
What does EVT identify?
Minimums and Maximums on a certain interval.
The limit definition of an integral
What is Lim h to 0 ((f(x+h)-f(x))/h)?
(d/dx)((2x^2+1)/(x^2-4)
what is -(18x)/(x^2-4)^2?
Int (1/cos^2(x))dx
what is tan(x)+C?
Lim x to ∞ (e^x)
what is ∞?
Fundamental theorem of Calculus (second part)
what is d/dx Int a to x (f(t))dt=f(x)?
Chain Rule
What is [f(g(x)]’=f’(g(x))g’(x)?
(d/dx)(ln(3x))
what is 1/x?
Int (5(sin(8x)cos(5x))dx
what is 5/2(-1/13(cos(13x)-1/3cos(3x))+C?
Lim x to e (e^x)
what is e^e?
Fundamental theorem of Calculus (first part)
What is Int a to b (f(x))dx=f(b)-f(a)?
What does the integral of velocity yield?
What is the displacement of the object?
(d/dx)(ln(x^3)3e^x)
what is 3((3e^x)/x+3e^xln(x))?
Int (3x^2(x^3+1)^6)dx
what is 1/7(x^3+1)^7)+C?
Lim x to 15 (ln(5)e^x)
what is ln(5)e^15?
What does the Fundamental theorem of Calculus require of a function to be applicable?
What is continuity?
y=f(x) where f(x) is decreasing while the rate is increasing. Describe f(x) concavity.
what is concave up?