[Math 132] - Final Exam Guide - Comprehensive Notes for the exam (51 pages long!)
Document Summary
4. 9 antiderivatives f(t) = model for a physical qty, i. e. temp in a room at time t f"(t) = instantaneous rate of change of f at t. Compute derivatives of the following functions: a. ) b. ) g(x) = 25x c. ) d. ) Def: f(t) is an antiderivative of f(t) if f"(t) = f(t) If f(t) is an antiderivative of f(t) then f(t) + c is also an antiderivative. F(t) + c is a general antiderivative of f(t) Class problems: find an antiderivative of: a. b. c, find the general antiderivatives from #1. Just add + c to all antiderivatives: find a function f such that. Compute area under y=f(x) x=a to x=b using n approximate rectangle: break [a,b] into subintervals of equal length. [x0,x1] [x1,x2] [x2,x3] [xn-1,xn] x0 is a x1 is a+ x, x2 is a+2 x until xn is b: select a sample point from each subinterval and evaluate f(xi. X=(b-a)/n: find area using limit definition of the derivative.
