Precalculus and Limits

Function composition, limits of algebraic functions, limits at infinity and infinite geometric series.

10 questions, free, marked as you go with a worked explanation on every one.

What this covers

Given f(x) = 2x + 1 and g(x) = x², evaluate the composite function (f ∘ g)(3).
Evaluate the limit of (x² - 4) / (x - 2) as x approaches 2.
Evaluate the limit of (3x² + 2x) / (x² - 5) as x approaches infinity.
Find the sum of the infinite geometric series 6 + 2 + 2/3 + 2/9 + ...
For which value of x is the function f(x) = (x² - 9) / (x - 3) discontinuous, and what kind of discontinuity is it?
Why does the limit of |x| / x as x approaches 0 fail to exist?
Which interval notation describes the set of all x such that -2 < x ≤ 5?
A population of bacteria in a limited environment is modelled by P(t) = 100t / (t + 5), where P is measured in thousands and t is the time in hours. What value does the population approach as t grows very large? Give your answer in thousands.
Evaluate the limit as x approaches 1 of (x^2 - 1) / (x - 1).
Evaluate the one-sided limit as x approaches 2 from the left of (x - 2) / |x - 2|.