MATH 3 Precalculus UCSC

1. (20 pts) Find the solution set: a) 6x 2(x 3) = 4(x + 1) + 4 b) 2 3x + 1 5 = 9 2. (10 pts) Graph the solution set to the inequality 2x + 5y < 10 . 3. (20 pts) Solve the inequality, express the solution set in interval notation and graph the solu

Name: _ 1 Class: Date: _ Set up, but do not evaluate, an integral for the area of the surface obtained by rotating y = ln x , 1 axis. 6 6 6 x 6 about the x a. 1 6 22 ln x dx c. 1 6 2 2 x dx 2 e. 1 2x 1+ 1 x 2 dx b. 1 2 x 1+x 2 dx

Name: _ 1 Class: Date: _ Use the method of cylindrical shells to find the volume generated by rotating the region bounded by curves y = 1 , y = 0, x = 4, x = 7 x about the y Problem code: stet. 06.03.03 2 Use the method of cylindrical shells to f

Basic Differentiation Formulas In the table below, ? 0 B and @ 1B represent differentiable functions of B Derivative of a constant Derivative of constant multiple Derivative of sum or difference Product Rule Quotient Rule .B . .B . .B ! (-?) - .

Practice for Exam 2 1. Use the definition of the derivative to find the derivative of f (x) at the indicated point: a) f (x) = x 2 x at x = 3 . b) f (x) = x at x = 16 . 2. Find the equation for the tangent line to the graph of y = f (x) : 1 a) f (x)

Name: _ 1 Class: Date: _ Which of the following integrals are improper? 6 11 2 a. 0 x x 2 dx c. 1 0 5x 10 e x 10 dx 13x + 42 5 dx 6 e. 5 sec x dx 10 b. 8 x x d. 8 1 x 2 dx +8 Problem code: stet. 07.08.01cm 2 Find the area unde

1. How do you find the intervals where a function is increasing? How do you find the intervals where a function is decreasing? Take the derivative of the function and determine where the derivative is positive and where the derivative is negative.