L'Hôpital's Rule can be applied multiple times to show how quickly different functions grow, proving that an exponential function like 'e to the x' grows infinitely faster than a polynomial like 'x squared'.
Solving a differential equation doesn't just give one answer, but an infinite family of solution curves; an 'initial value' is the key that unlocks the single, unique curve from that family that fits a specific scenario.
A shortcut when solving definite integrals with u-substitution is to change the integral's limits to match the new variable, allowing you to skip the final step of substituting back.
The 'Root Test' in calculus is a specialized tool that is most effective for testing infinite series where terms are raised to the nth power, because the test itself involves taking an nth root.
The harmonic series, which is the sum of fractions 1 + 1/2 + 1/3 + 1/4 and so on, surprisingly adds up to infinity, even though the terms being added get smaller and smaller.
