Limits
lim x->infinity (x^2-2/3x^2+2)
What is 1/3
d/dx(x^3 + 4x^2 +7x + 3)
What is 3x^2+8x+7
integral (x^2+3)dx
What is 1/3x^3+3x+C
dy/dx for x^2+y^2=36
What is -x/y
Constant Rule
The derivative of a constant equals 0
lim x-> -infinity (x^3-x^2+3/2x^3-x-7)
What is 1/2
d/dx((x^2+1)(x-2))
What is 3x^2-4x+1
integral (x^4-4x^2+7)dx
What is 1/5x^5-1/34x^3+7x+C
dy/dx for y^6+3y=x^2
What is 2x/3(2y^5+1)
Part 1 of the fundamental theorem of calculus
What is the integral from a to b f(x)dx = F(b)-F(a)
lim x->infinity (sqrt(x^2+16)/x+4)
What is 1
d/dx((2x^3+4x)/(x-3)^2)
What is (2(2x^3-9x^2-6))/((x-3)^2)
integral (x^3/sqrt(x^2+16))dx
What is ((x^2-32)(sqrt(x^2+16)))/3 +C
dy/dx for cos^3x+sin^2y=1/3
What is 3cos^2xsinx/2sinycosy
Part 2 of the fundamental theorem of calculus
What is the derivative of the integral from a to u(x) f(t)dt = f(u(x)) * u'(x)
lim x->3 (x^2-9/x-3)
What is 6
d/dx((x^4+6)^2)
What is 8x^3(x^4+6)
integral (lnx)/x dx
What is (lnx)^2/2 +C
dy/dx for 1/x+lny=2x
What is 2y+y/x^2
L'Hopital's Rule
What is the method used to find the limit of a function of a 0/0 or infinity/infinity condition
lim x->4 (2x^2-32/x^3-64)
What is 1/3
d/dx(e^(2x^2+3x))
What is (4x+3)(e^(2x^2+3x))
integral (1-sin^2x)(secx) dx
What is sinx + C
dy/dx for (xy)^2+1/x-lny=5x
What is (5x^2y+y-2x^3y^3)/(x^2(-1+2x^2y^2))
A hypothesis in Rolle's Theorem
What is "f is continuous on the closed interval [a, b]" OR "f is differentiable on the open interval (a, b)" OR "f(a) = f(b), then there is a number c in (a, b) such that f'(c) = 0"