MATH 31A (Butler) Midterm II, 19 February 2010 1. Find the unique value c that satises the Mean Value Theorem for the function f (x) = arctan(sin x) for x between a = 0 and b = /2. (Your answer will involve an arcsin or arccos term. Hint: sin2 x + cos2 x
MATH 31A (Butler) Practice for Final (B) Try to answer the following questions without the use of book, notes or calculator; but you can use the equation sheet posted on the course website. Time yourself and try to nish the questions in less than three ho
MATH 31A (Butler) Practice for Final (A) Try to answer the following questions without the use of book, notes or calculator; but you can use the equation sheet posted on the course website. Time yourself and try to nish the questions in less than three ho
Math 1 Practice Problems for the Final EXAM Fall 2009 Name _ UCLA ID# _
Read the instructions carefully. One of the skills being tested is your ability to read and understand mathematics questions. Show all of your work . Allow the grader to see how you g
Final Review
Material from the previous midterms The nal is cumulative but will not include problems about limits, curve sketching and Riemann sums. More information about what we covered can be found in the previous midterm reviews. This review will only
MATH 31A (Butler) Practice for Midterm IIa (Solutions)
1. (a) Use linearization to give an estimate for
3 1017.
We rst note that 3 1017 is close to 3 1000 = 10 and so we can use lineariza tion for the function f (x) = 3 x = x1/3 at x = 1000. Before we s
MATH 31A (Butler) Practice for Midterm IIa (Solutions)
1. (a) Verify that (2, 1) is a critical point for the curve y 3 x 3yx2 = x2 15x + 16. (You need to verify two things: (i) it is on the curve and (ii) it is a critical point.) To verify it is a point o
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Student name: Student ID: TAs name and/or section: MATH 31A (Butler) Midterm I, 22 January 2010 This test is closed book and closed notes. No calculator is allowed for this test. For full credit show all of your work (legibly!). Problem 3 is worth 15 pts,
Midterm 2 Review
Material from the previous midterm The midterm is not cumulative but you are expected to know the following important facts: d (1) = 0 dx da (x ) = axa1 dx d f (x) + g (x) dx d k f (x) dx d f (x)g (x) dx = f (x) + g (x) = kf (x) = f (x)g
Midterm 1 Review
Rate of change We are interested in nding the rate of change of a function. In particular, given a function y = f (x) we are interested in nding how fast y is changing with respect to x at some xed time x = a. The main way we will do this
MATH 31A (Butler) Practice for Final (C) Try to answer the following questions without the use of book, notes or calculator; but you can use the equation sheet posted on the course website. Time yourself and try to nish the questions in less than three ho