The slope of a tangent line to a curve. A secant to a curve. The difference quotient. The derivative of f(x)= x2.
What is the derivative definition ?
100
finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known. The rate of change is usually with respect to time.
What is Related Rate definition ?
100
d/dx{tanx}=
What is sec²x ?
100
Formula for acceleration given v(t):
What is v(b)-v(a)/b-a
100
b
∫ f(x)+g(x)dx=
a
b b
What is ∫ f(x)dx + ∫ g(x)dx ?
a a
200
d/dx(xⁿ)=
What is nxⁿ⁻¹ ?
200
V=4/3πr³
dV/dt= ?
What is 4πdr/dt r² ?
200
d/dx{cscx}=
What is -cscxcotx ?
200
Total distance formula
What is ∫lv(t)ldt ?
200
a
∫ f(x)dx=
a
What is 0 ?
300
h(x)=f(x)g(x)
h'(x)=g(x)f'(x)+f(x)g'(x)
What is Product Rule ?
300
The radius of a circle is decreasing at a constant rate of .1 cm per second. In terms of circumference C, what is the rate of change of the area in sq. cm per second?
What is -0.1 C
300
d/dx{cosx}=
What is -sinx ?
300
Formula for Position at b:
b
What is s(b)=s(a)+∫ v(t)dt ?
a
300
∫1/x dx =
What is l(lnx)l ?
400
The limit derivative definition
What is dy/dx=lim(h->0) f(x+h)-f(x)/h
400
When x=8, the rate at which 3√x is increasing is 1/k times the rate at which x is increasing. What is the value of k?
What is k=12 ?
400
d/dx{arcsinx}=
What is 1/√(1-x²) ?
400
Compute the particle's velocity at t = 1, 2, and 4 seconds.
s = f(t) = t4 – 2t3 – 6t2 + 9t
What is v(1) = –5 in/sec, v(2) = –7 in/sec, v(4) = 121 in/sec ?
400
Formula for Finding Total Amount:
b
What is f(b)= f(a)+ ∫ f'(x)dx ?
a
500
f(x)=4x³-3x²+2x-π
f'(x)= ?
What is 12x²-6x+2 ?
500
Let f(x)= √x . If the rate of change of f at x=c is twice its rate of change at x=1, the c= ?
What is c=1/4 ?
500
d/dx{arccscx}=
What is 1/lxl(√x²-1) ?
500
If the position of a particle is given by x(t)=100−16t 2
x(t)=100−16t2, find the position of the particle when the velocity is zero.