Final answer:
To simplify the difference quotients [f(a + h)-f(a)]/h and [f(x)f(a)]/(x-a) for f(x) = 5/2 and a = 2, substitute the given values and perform the calculations.
Step-by-step explanation:
To simplify the difference quotients [f(a + h)-f(a)]/h and [f(x)f(a)]/(x-a) for f(x) = 5/2 and a = 2, we will substitute the given values into the expressions and simplify.
For the expression [f(a + h)-f(a)]/h, we substitute f(x) = 5/2, a = 2, and perform the calculations:
[f(a + h)-f(a)]/h = [(5/2)(2 + h) - (5/2)(2)]/h = (5h/2)/h = 5/2
For the expression [f(x)f(a)]/(x-a), we substitute f(x) = 5/2, f(a) = 5/2, x = a + h, and perform the calculations:
[f(x)f(a)]/(x-a) = [(5/2)(5/2)]/[(a + h) - a] = (25/4)/h = 25/(4h)