Limits
Evaluate:
limx→3 (2x+1)
What is 7?
Find the derivative of:
f(x) = x3
What is 3x2?
If f'(x) > 0 on an interval, the function is this.
What is increasing?
Evaluate
Intergal 4x3dx
What is x4+C?
If:
dy/dx= 3x2find y.
What is x3+C?
Evaluate:
limx→2 (x2+4x−1)
What is 11?
Find the derivative of:
f(x) = 5x4-2x
What is 12x3-2?
If f"(x) > 0, the graph is described as this.
What is concave up?
Evaluate
Intergal cosxdx
What is sinx+C?
A differential equation that includes dy/dx is used to describe this.
What is rate of change?
Evaluate:
limx→0 (sinx)/x
What is 1?
Differentiate:
f(x) = sinx
What is cosx?
A point where the derivative equals zero or is undefined is called this.
What is critical point?
Evaluate
Integral xdx
a=0 b=2
What is 2?
Find the particular solution if:
dy/dx=2x
and y = 3 when x = 0.
what is y=x2+3?
Evaluate:
lim x→1 (x2-1)/(x-1)
What is 2?
Differentiate:
f(x) = ex
Find the slope of the tangent line to:
f(x) =x2+1
at x = 3
What is 6?
Find the area under:
f(x) = x2
from x = 0 to x = 1.
What is 1/3?
Solve:
dy/dx= 1/x
What is y=ln|x|+C?
Find the horizontal asymptote of:
f(x)= (3x2+1)/(x2-4)
What is y=3?
Use the product rule to differentiate:
f(x) =x2cos x
What is 2xcosx-x2sin x?
A particle's position is:
s(t) = t3-6t2+9t
Find the velocity at t = 2.
What is -3?
Evaluate
Integral (3x2-4x+1)dx
What is x3-2x2+x+C?
A population grows according to:
dP/dt= 0.2P
This type of growth is called this.
What is exponential growth?