Questions with Solution - Elementary Calculus I | MATH 220 | Study notes Calculus

Calculus 220, sections 0.3–0.6 Stuff You Need to Know

notes by Tim Pilachowski

I hope to have notes for each lecture posted on my math department website, http://www.math.umd.edu/~tjp,

prior to the lecture itself. Feel free to print out and/or download each of these and bring it with you to class. In

this way you can put your attention on listening and thinking, and only need to write all those little “extras” that

will come up during my presentation. Need I tell you that these notes will be an outline only, and that they

cannot replace your presence in the lecture?

Be sure to attend the discussions on a regular basis, too. You’ll find them to be valuable in cementing the topics

covered in the lecture. You’ll get the most out of the discussion if you do the assigned homework before the

discussion, and participate in all the discussion activities.

To help you get up to speed for Math 220, we’re going to spend this first class going over some things I assume

you already know, but about which you may need a little reminder. The assigned practice exercises are from the

Chapter 0 Supplementary Exercises. I leave it to you to go back on your own to topics and exercises on which

you personally need some more review. Also, go to the Math Dept. Testbank (http://db.math.umd.edu/testbank/)

and get some final exams from recent semesters of Math 113. You need to know how to do all of these

questions.

Include a review of adding & subtracting and multiplying & dividing fractions and decimals. Computations on

tests will involve only fairly easy numbers, and an exact answer will be required rather than a decimal

approximation.

Example A (evaluating functions): Given

(

)

2+−= xxxf , find ⎟

⎠

⎞

⎜

⎝

⎛−3

f. Answer: 9

I suggest you first rewrite the formula using parentheses to create blank spaces which you then fill in.

You’ll also need to know how to graph functions both by hand and with a calculator, as well as be able to read

and interpret graphs. Using shifts and translations will come into play.

Example B (domain and range): Given

()

43 +−= xxg state the domain and range. Answers: x ≤ 3; y ≥ 4

We’ll be doing a good bit with linear functions. We’ll review these extensively in our investigation of slope in

section 1.1.

Example C (quadratic functions): Find the vertex, y-intercept, and any x-intercepts of .

()

2+−= xxxf

Answers:

(

)

1, , (0, 1), none

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Calculus 220, sections 0.3–0.6 Stuff You Need to Know

notes by Tim Pilachowski

I hope to have notes for each lecture posted on my math department website, http://www.math.umd.edu/~tjp, prior to the lecture itself. Feel free to print out and/or download each of these and bring it with you to class. In this way you can put your attention on listening and thinking, and only need to write all those little “extras” that will come up during my presentation. Need I tell you that these notes will be an outline only, and that they cannot replace your presence in the lecture?

Be sure to attend the discussions on a regular basis, too. You’ll find them to be valuable in cementing the topics covered in the lecture. You’ll get the most out of the discussion if you do the assigned homework before the discussion, and participate in all the discussion activities.

To help you get up to speed for Math 220, we’re going to spend this first class going over some things I assume you already know, but about which you may need a little reminder. The assigned practice exercises are from the Chapter 0 Supplementary Exercises. I leave it to you to go back on your own to topics and exercises on which you personally need some more review. Also, go to the Math Dept. Testbank (http://db.math.umd.edu/testbank/) and get some final exams from recent semesters of Math 113. You need to know how to do all of these questions.

Include a review of adding & subtracting and multiplying & dividing fractions and decimals. Computations on tests will involve only fairly easy numbers, and an exact answer will be required rather than a decimal approximation.

Example A (evaluating functions): Given f ( x ) = x^2 − x + 1 , find ⎟

f. Answer : 9

I suggest you first rewrite the formula using parentheses to create blank spaces which you then fill in.

You’ll also need to know how to graph functions both by hand and with a calculator, as well as be able to read and interpret graphs. Using shifts and translations will come into play.

Example B (domain and range): Given g ( ) x = 3 − x + 4 state the domain and range. Answers : x ≤ 3; y ≥ 4

We’ll be doing a good bit with linear functions. We’ll review these extensively in our investigation of slope in section 1.1.

Example C (quadratic functions): Find the vertex, y -intercept, and any x -intercepts of f ( ) x = x^2 − x + 1.

Answers : ( 21 , 43 ), (0, 1), none

Example D: Find the vertex, y -intercept, and any x -intercepts of h ( x ) = 2 x^2 − 5 x − 3.

Answers : ( 45 , − 498 ); ( 0 , − 3 ) ;(− 21 , 0 )& (3, 0)

Example E (zeroes of functions): Find the zeroes of h ( x ) = 2 x^3 − 5 x^2 − 3 x. Answers : 0, − 21 and 3

Note the connections among factors (which are formulae or equations), x -intercepts (which are points), and zeroes (which are numbers or values). You’ll also need to be familiar with polynomial functions, rational functions, and asymptotes for chapter 2.

Example F (composition of functions): Given f ( x ) = x^2 − x + 1 and m ( x ) = x − 2 , find ( f o m )( x ).

Answer : x^2 − 5 x + 7

Composition of functions becomes extremely important beginning in chapter 3.

Example G: Given f ( ) x = x^2 − x + 1 , evaluate the difference quotient

f x + h − f x

. Answer : 2 x + h – 1

Example H (exponent properties): Simplify

x x

. Answer : 8 x^2 x

Questions with Solution - Elementary Calculus I | MATH 220, Study notes of Calculus

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Download Questions with Solution - Elementary Calculus I | MATH 220 and more Study notes Calculus in PDF only on Docsity!

Calculus 220, sections 0.3–0.6 Stuff You Need to Know

Example A (evaluating functions): Given f ( x ) = x^2 − x + 1 , find ⎟

Example B (domain and range): Given g ( ) x = 3 − x + 4 state the domain and range. Answers : x ≤ 3; y ≥ 4

Example C (quadratic functions): Find the vertex, y -intercept, and any x -intercepts of f ( ) x = x^2 − x + 1.

Example D: Find the vertex, y -intercept, and any x -intercepts of h ( x ) = 2 x^2 − 5 x − 3.

Answers : ( 45 , − 498 ); ( 0 , − 3 ) ;(− 21 , 0 )& (3, 0)

Example E (zeroes of functions): Find the zeroes of h ( x ) = 2 x^3 − 5 x^2 − 3 x. Answers : 0, − 21 and 3

Example F (composition of functions): Given f ( x ) = x^2 − x + 1 and m ( x ) = x − 2 , find ( f o m )( x ).

Example G: Given f ( ) x = x^2 − x + 1 , evaluate the difference quotient