{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture 9 Notes (MATH M-119; Brief Survey of Calculus I, Staff)

Lecture 9 Notes (MATH M-119; Brief Survey of Calculus I, Staff)

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: KW”) 7:6? UJW‘ SK \2.“\ 1.9 Proportions and Power Functions Power Functions y = Rx? . Note that polynomials are the sums of power functions (which makes a power function also a polynomial). Determine if the following are power functions and if so, find k and p 5 y = E; y = 16x _ i y 2x “a 2-: y 3 y — (3x3): x y = 23: +1 Proportionality Ex (13) The energy, E, expended by a swimming dolphin is proportional to the cube of the speed, v, of the dolphin. ,1) a = v V If a dolphin uses 500 caloriesfhour swimming at 20 mph, how many calories per hour W111 it use sw1mm1ng 30 mph? so.) 940‘) ‘ , if H‘s-’1 4‘1 500 7' ‘4 Us" $9 .14 r "" - U: — .001: » r.‘ ‘1- »ti’» #277”: “’5 ‘l ' ‘L 4W" g, L €60 {Ll} P “"1." . IAN”. "i“ a? a— he,“ ' 0:01 5 \‘V’ _‘--i 4/ “1&0 L\'{ L K319 (“fitVL/fi 120‘1l‘f/";.1U“ 3 [ON a\ l} \ \L , «mm/1;..3- " 8 T- ‘. oh» 1 5 ‘4 Le" ‘ ’ V/ i “r r\ We“) : . sumo)" A \ #\q’] E f D C} \l\ a ‘5 H95? 7 5 (gt/Hoot?— A directly proportional function will look like y=k*(?), while an inversely proportional function will look like: y=k*1;’(?) (note that the k is never flipped). Ex (19) Biologists estimate that the number of animal species of a certain body length is inversely proportional to the square of the body length. A) Write a formula for the number of animal Species, N, of a certain body length as a function of the length, L. N = WA B) If there are 100 species that are 20 feet long, according to the formula, how many species are 1 inch long? . } ‘z lw=nlw w: qasoo l N a seam ‘ AL .. 1“ :— N :qoooo ("i/(W23) mice {’3' 6303,5300 Polynomials Most of you already know what a polynomial is, but we want to clarify some Hi“ we definitions. Let’s take as an example: f(x) = 4x2 +2x —3x“ +4 : fly“ 4 ti? +2»; “4/7 Law I 1) the degree of a polynomial is the highest power that you See in the problem 2) the leading coefficient is the number in front of the x with the highest power If we look at the graph up close, we see several things going on. The power ofa polynomial is at least one more than the number of local extrema “bumps or turning points ” V f\ 14 o ' a -. — A /\ 3 Mm: f umjibwlf «ixsnu manna; A 1‘ /\ f P w/ /Q/E?613UMLS 7 \1 _§\fi When we look at it zoomed out, it just looks like the power fimction consisting of the leading coefficient and x to the degree. Note that if the degree of the polynomial is Odd: Even: The leading coefficient also has an effect. The macro effect is only determined by the sign: What do an odd and even graphs look like if the leading coefficient is negative? So in the short run, a large leading coefficient will make the graph grow fast, but in the long run, the growth is determined by: m at =33:- “‘“=="':‘1€« 2:} 2, =32 ~ 22532:“ Ugh—212m 53-2 2 2:4 w 2 02’sz 9227321253” “Mums (i?) [6%er (2:) AS X CJG‘S “ ”a? f CW) =1: lavvgé' US") M 22.242222 (9] ...
View Full Document

{[ snackBarMessage ]}