What is the equation to find the slope of a tangent line?
M= lim f(c+Δx)-f(c)
Δx—>0 Δx
100
What is 1+cot^2(x)?
csc^2(x)
100
What is the formula of a sphere to find the volume?
V=(4/3)πr^3
100
What is the differentiation rule for constant rate?
f(x)=c ——> f′(x)=0
100
What are the four different notations for a derivative?
They are:
f′(x) y′ dy/dx d/dx [f(x)]
200
What is the slope of the tangent line
f(x)= 2x-3?
2
200
What is d/dx [secx]?
tan(x)*sec(x)
200
What is the volume formula of a cone?
V=(1/3)πr^2h
200
What is the product rule?
d/dx [u*v]= u*v′+u′*v
200
What is the notation for higher order derivatives?
They are:
f′′(x) y′′ and f′′′(x) y′′′
300
The x-values at these special points (relative min, relative max, where f'(c)=0, f'c=DNE) are ________?
critical numbers
300
Solve for y=sec(x)/x.
tan(x)^2-sec(x)/(x)^2
300
The radius of a sphere is increasing at a rate of 3 in/min. Find the rate of change of the volume when r=9 inches.
When r=9 inches the rate of change is 972 in^2/min.
300
What is the quotient rule?
d/dx [f(x)/g(x)]= f′(x)*g(x)-f(x)*g′(x)/ [g(x)]^2
300
What is the notation for the position, velocity, and acceleration function?
Position: S(t)
Velocity: V(t)
Acceleration: A(t)
400
How can I find the equation of a tangent line at a given point?
1st: find f′(x)
2nd: plug the x-value into f′(x)
3rd: use the point slope equation
400
What is ∫csc^2(x)dx?
-cot(x)+c
400
Find the rate of change
Equation: V=(4/3)πr^3
Rate: dr/dt=3 cm/min
Find: dv/dt when r=36cm
When r=36cm, the rate of change of the volume is
15,552π cm^3/min.
400
What is the chain rule?
d/dx [f(g(x))]= f′(g(x))*g′(x)
400
What is the test for concavity?
1.) If f"(x)>0 for all x in (a,b), then the graph of f(x)is concave upward on (a,b).
2.) If f"(x)<0 for all x in (a,b), then the graph of f(x)is concave downward on (a,b).
500
Find the equation of the tangent line at the given point,
f(x)=x^2-4x+5 (4,5)
The equation of the tangent line at the given point is
y=4x-11.
500
Find the indefinite integral
∫(-6sinx-7cosx)dx.
6cosx-7sinx+c
500
A conical paper cup is 10 cm tall with a radius of 8 cm. The cup is being filled with water so the water level rises at a rate of 2 cm/sec. At what rate is the water being poured into the cup when the water level is 9 cm?
When the water level is 9 cm the rate that is being poured at is 7776/75 cm^3/sec.
500
What is L'Hopital's rule?
If lim (f(x)/g(x)) =0/0 as x-approaches c then,
lim (f(x)/g(x)) = lim (f'(x)/g(x)) as x approaches c.