Practice Limiting Cases in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Extreme values of a parameter (approaching zero, infinity, or a critical threshold) used to check formulas and reveal simplified behavior.
What happens when things get really big, really small, or reach boundaries?
Example 1
easyThe formula for the sum of a geometric series S = \frac{a(1-r^n)}{1-r} (r\ne 1). Find the limiting case as n \to \infty when |r| < 1.
Example 2
mediumThe compound interest formula is A = P(1+r/n)^{nt}. Analyse the limiting cases n=1 (annual), n=12 (monthly), and n \to \infty (continuous).
Example 3
easyFor the area of a regular n-gon inscribed in a circle of radius r: A_n = \frac{n}{2}r^2\sin(2\pi/n). What does A_n approach as n \to \infty?
Example 4
mediumThe binomial (1+x/n)^n has a famous limiting case. Evaluate for n=1, 2, 10, 100 with x=1 and identify the limit.