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MATH 160  Boise State Study Resources

Definite Integrals
School: Boise State
Course: Survey Of Calculus
3 1 V = t2 +1 8 When we find the area under a curve by adding rectangles, the answer is called a Rieman sum. 2 1 The width of a rectangle is called a subinterval. 0 1 2 subinterval 3 4 The entire interval is called the partition. partition Subintervals do

Exam 2 Review
School: Boise State
Course: Survey Of Calculus
Exam 2 Review: 2.83.6 This portion of the course covered the bulk of the formulas for dierentiation, together with a few denitions and techniques. Remember that we also left 2.8 for this exam. From 2.8, we should be able to plot the derivative given a gr

Exam 1 Summary
School: Boise State
Course: Survey Of Calculus
Summary: To Exam 1 (Up through 2.7) General Background: Chapter 1 and Appendices There is a lot of algebra and trigonometry in Chapter 1, and Appendices A, B, C and D, so this is not an exhaustive list of everything you need to know, but there are some th

Exam 1 Review
School: Boise State
Course: Survey Of Calculus
Exam 1 Review Questions 8. Show that there must be at least one real solution to: x5 = x2 + 4 Please also review the old quizzes, and be sure that you understand the homework problems. General notes: (1) Always give an algebraic reason for your answer (gr

Derivatives Of Trig Functions
School: Boise State
Course: Survey Of Calculus
Consider the function y = sin ( ) slope We could make a graph of the slope: 2 0 Now we connect the dots! 2 The resulting curve is a cosine curve. 1 0 1 0 1 d sin ( x ) = cos x dx We can do the same thing for y = cos ( ) slope 2 0 The resulting curve is

Exam 3 Review
School: Boise State
Course: Survey Of Calculus
Math 125: Exam 3 Review Since were using calculators, to keep the playing eld level between all students, I will ask that you refrain from using certain features of your calculator, including graphing. Here is the statement that will appear on the exam an

Parametric Equations
School: Boise State
Course: Survey Of Calculus
There are times when we need to describe motion (or a curve) that is not a function. We can do this by writing equations for the x and y coordinates in terms of a third variable (usually t or ). x = f (t ) y = g (t ) These are called parametric equations.

Rates And Changes
School: Boise State
Course: Survey Of Calculus
The slope of a line is given by: y x The slope at (1,1) can be approximated by the slope of the secant through (4,16). 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 y 16 1 15 = = =5 x 4 1 3 We could get a better approximation if we move the point closer to (1,1)

Limit Of A Function
School: Boise State
Course: Survey Of Calculus
S ECTION 2.2 THE LIMIT OF A FUNCTION each quantity, if it exists. If it does not exist, explain why. (a) lim t t (b) lim t t (c) lim t t (b) lim f x x l 3 xl4 4. For the function f whose graph is given, state the value of each quantity, if it exists. If

Extra Trig Practice
School: Boise State
Course: Survey Of Calculus
Extra Practice: Trigonometry 1. Evaluate the following (exactly, without a calculator): (a) sin(3/4) (c) tan(2/3) (e) csc(29/6) (b) cos(5/4) (d) sec(7/6) (f) tan(/4) 2. What is the amplitude, period and frequency for f (x) = 1 + 2 cos(3x) 3. What is the p

Review For Exam 2
School: Boise State
Course: Survey To Calculus
Review for Exam 2 Covers: section 3.6, 3.7 & 4.1 4.5 Math 160, Fall 12 Section 3.6: Be able to calculate x , y , y / x , dx, and dy for a given function and xvalues Section 3.7: Be able to find marginal cost, marginal revenue, and marginal profit funct

Test 3 Sols1
School: Boise State
Name: _ Test #3 Applications of Derivatives Math 160 Calculators are permitted, but show all work. 1. Solve either of the problems below. A. A boat is tied to a dock as shown in the picture below. A winch on the dock is connected to the boat, and when the

Test 3 Sample_1
School: Boise State
Sample Test This test will cover 4.45.6, excepting 4.6 (Related Rates, which we skipped) This is probably longer than the actual test will be. Part I 1. Find y' for y =e x 3. 2 2. Find f x =ln 3x 1 Find f'(x) 4. dy for dx x 2 y 2=25 x 2 y 2e xy= 20 Find

Test 2
School: Boise State
Name: _ Test #2 Limits, Continuity & Derivatives Find the derivative of the following functions: 1 x3 1. f x = x 10 2. g x = 4. h x =25 5. f t = ln t 6. f x =12 x 7. f x =3 x 8. V x = 2 9. r s =log 5 s 10. f x = x ln x x 11. y = 3. y =e x 5 x 3 x 2 2 x 1

Test 2 Sols
School: Boise State
Name: _ Test #2 Limits, Continuity & Derivatives Find the derivative of the following functions: f ' x =10 x 1 x3 3 4 g ' x = 4 =3 x x 2. g x = 1. f x = x 10 9 4. h x =25 5. f t = ln t h ' x =0 f ' t =1 / t 7. f x =3 x x 10. f x = x ln x x y ' =e x 6. f

Take Home Final1
School: Boise State
Name: _ Math 160 Final Exam Takehome portion Calculators are permitted. Please show all necessary steps, including setting up integrals. Part I (Test 2) 1. Use the definition of the derivative (i.e., the four step process) to find the derivative of the f

Implicit Extra Credit
School: Boise State
Extra Credit The Folium of Descartes is a famous curve that looks something like this: It is the graph described by the equation x 3 y 3= 3 xy . You can see that there is a point on this graph where the tangent line is horizontal, and a point where it is

Final
School: Boise State
Name: _ Math 160 Final Exam Business Calculus Part I 1. Limits and Continuity cfw_ x 2 5 x 6 g x = x 2 2 x 3 a x 3 x =3 What value of x makes g continuous at x = a? Using this value for a, is g continuous everywhere? (i.e., are there any other discontinui

Final Takehome(1)1
School: Boise State
Name: _ Final Exam Take home portion. Please show all work. This is a calculus test, so I need to see calculus work. If you use a calculator to evaluate an integral, you need to show it set up. 1. Nonbuoyant bulls and cows need to be pastured separately

Test 3 Sols
School: Boise State
Name: _ Test #3 Part I (40 points) Find the derivative: 1. Find f ' x for f x =e x x 25 3 f ' x =e x 6 x x 2 5 2 y ' for x 2 y 2=1 xy 2 y y ' = 2 = x xy 2. Find dy for dx dy 2 x e y = dx xe y 1 y 3. Find 2 x e y = x 2 Find the limit 2 4. lim x 1 x x ln x

Test 3 Spring 2011
School: Boise State
Name: _ Test #3 Applications of Derivatives Math 160 Calculators are permitted, but show all work. 1. Solve either of the problems below. A. A boat is tied to a dock as shown in the picture below. A winch on the dock is connected to the boat, and when the

Review For Exam 11
School: Boise State
Course: Survey To Calculus
Review for Exam 1 Covers: section 1.1, 1.2, 2.1, 2.3 & 3.1 3.5 Math 160002, Fall 12 Section 1.1: Be able to solve a linear equation Be able to solve a linear inequality Section 1.2: Be able to graph a linear function Be able to find the slope of a li

Test 4_1
School: Boise State
Test #4 Integrals Chapters 67 Takehome test Part I: evaluating integrals Evaluate the integrals. Show all work. Give answers either as exact answers, or rounded to the nearest hundredth. 1. x 2 1 x dx 3. 1 x x 3 dx 5. 6 x x 3 dx 6 1 2. e 3 t dt 4. 0 x

Test 4
School: Boise State
Name: _ Math 160 Test #4: Integration For the problems marked Calculatorfree, no calculators may be used. You must show all work for these problems so that I can see, step by step, how it is done. Part I: Antiderivatives Find the antiderivative or inte

Test 4 Takehome
School: Boise State
Name: _ Test #4: Integrals Takehome portion Calculators Allowed. Show the setup for the integrals, but you can use the calculator to evaluate it. 1. A computer running a Microsoft operating system will experience its first Blue Screen Of Death 4t (BSOD)

Test 4 Takehome Sols
School: Boise State
Name: _ Test #4: Integrals Takehome portion Calculators Allowed. Show the setup for the integrals, but you can use the calculator to evaluate it. 1. A computer running a Microsoft operating system will experience its first Blue Screen Of Death 4t (BSOD)

Test 4 In Class
School: Boise State
Name: _ Test #4 Integrals Inclass portion No Calculators 1. 4 0 t 1 dt 2 t 1 2 2 Find the average value of this function over the interval [0, 4] dy =x2 y dx 2. Find the general solution to the equation Find the particular solution to the equation that

Test 4 In Class Sols
School: Boise State
Name: _ Test #4 Integrals Inclass portion No Calculators 1. The easiest thing to do here would be to split it up. The first part needs usubstitution, but not the second part. 4 4 4 t t 0 2 t 21 2 1 dt =0 2 t 21 2 dt 0 1 dt 2 u = 2 t 1 ; du =4 t dt 1 9 u

Test 3
School: Boise State
Name: _ Test #3: Applications of Derivatives Math 160 This is a calculus test. I need to see calculus in order to give credit. Show all work. If I don't see calculus work, I won't give credit. 1. f is continuous and a < b < c < . < k < l < m x a b c d e f

160 Test 2 Derivatives Revised
School: Boise State
Name: _ Math 160 Test #2: Limits, Continuity and Derivatives Find the derivative of the function: 1. f ( x) = 6 x 10 2. h(t ) = ln(t ) 3. m(k ) = 5ke k 4. r (t ) = 10 t + t 10 5. p ( s) = log 2 ( s) 6. g ( x) = 3 9. Q(r ) = r 2 + 2r 5r 2 7. s (t ) = 1 t3