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LHospitals Rule f and g differentiable,
g?(a) ? 0 near a (except possibly at a). If

(indeterminate form of type
) or

(indeterminate form of type ) then

(if this limit exists).
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Indeterminate Product If

(indeterminate form of type ) then use
LHospital Rule for
Indeterminate Difference If

(indeterminate form of type ) then
try to convert into quotent and use LHospital
Rule.
Indeterminate Power If

(indeterminate form of type ) or

(indeterminate form of type ) or

(indeterminate form of
type ) then use
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Differential equation Equation that contains
an unknown function and some of its
derivatives. Order of differential equation
order of highest derivative in equations. f(x)
solution of differential equation, if it
satisfies the equation for all x in some
interval. Solve differential equation find ALL
possible solutions. Condition of the form
y(t0)y0 initial condition. Initial-value
Problem (IVP) find solution that satisfies the
given initial condition.
Separable equation 1st order differential
equation in which expression for dy/dx can be
factored as a function of x times a function of y
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Mixing problem A tank contains 20 kg of salt
dissolved in 5000L of water. Brine that contains
0.03 kg of salt per liter of water enters the
tank at a rate of 25L/min. The solution is kept
throughly mixed and drains from the tank at the
same rate. How much salt remains in the tank
after half an hour?