Practice Specialization in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Applying a general theorem or formula to a specific case by substituting particular values for the variables or parameters.
What does this general statement say about MY specific situation?
Example 1
easyThe Binomial Theorem states (a+b)^n = \sum_{k=0}^{n}\binom{n}{k}a^{n-k}b^k. Specialise to a=1, b=1 and a=1, b=-1 to obtain two identities.
Example 2
mediumThe AM-GM inequality states: for positive reals a,b, \frac{a+b}{2} \ge \sqrt{ab}. Specialise to a = x^2 and b = \frac{1}{x^2} (for x \ne 0) and state what you get.
Example 3
easyThe general formula for the sum of a geometric series is S_n = \frac{a(r^n-1)}{r-1}. Specialise to a=1, r=2 and compute S_5.
Example 4
mediumThe general derivative rule is (x^n)' = nx^{n-1}. Specialise to find the derivatives of x^3, x^{1/2}, and x^{-1}.