If the limit of a function is indeterminate then you can take the derivatives of the top and bottom functions separately in order to get the actual limit
What is the L'Hospital's Rule?
400
f (x) = (e^x)/x
f ' (x) = (e^x)/x - (e^x)/(x^2)
400
Find dy/dx of ytan(x+y) = 4
y/x
400
Find the antiderivative of xe^(-x^2)
(-1/2)e^(-x^2)
400
lim x->4 of (x - 4)^3 / l4 - xl
0
400
If f is differentiable for all values of x in (a, b) and f is continuous at x=a and x=b, then there's at least one number x=c in (a, b) such that f'(c) = [f(b) - f(a)] / b-a
What is the Mean Value Theorem?
500
f (x) = e^(lnx^2) - 3(x^-7)
f ' (x) = (2e^lnx^2)/x + 21/(x^8)
500
Find the solution when dy/dx = cos(x) / y^2 , where y(π/2) = 0
y = (3 sin(x) - 3)^(1/3)
500
Find the antiderivative of (x^2)(e^5x)
[(x^2) - (2x/5) + (2/25)]*[(e^5x)/5]
500
lim x-> 0 of (x + 4x^2 + sinx)/(3x)
2/3
500
If f is differentiable for all values of x in (a, b) and f is continuous at x=a and x=b, and f(a) = f(b) = 0, then there's at least one number x=c in (a, b) such that f'(c) = 0