By By (author) Bob Miller
With Bob Miller at your aspect, you by no means need to be clueless approximately math back!
Algebra and calculus are tricky on highschool scholars such as you. Professor Bob Miller, with greater than 30 years' educating adventure, is a grasp at making the advanced easy, and his now-classic sequence of Clueless research aids has helped tens of hundreds of thousands comprehend the cruel subjects.
Calculus-with its integrals and derivatives-is recognized for tripping up even the fastest minds. Now Bob Miller-with his 30-plus years' event instructing it-presents highschool calculus in a transparent, funny, and interesting way.
Read or Download Bob Miller's High School Calc for the Clueless - Honors and AP Calculus AB & BC PDF
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Extra info for Bob Miller's High School Calc for the Clueless - Honors and AP Calculus AB & BC
Y ϭ f(t ϩ ⌬t) Ϫ f(t) ϭ (t ϩ ⌬t)2 ϩ 5(t ϩ ⌬t) Ϫ (t2 ϩ st)t ϭ 3; ⌬t ϭ 5 Ϫ 3 ϭ 2 ϭ t2 ϩ 2t ⌬t ϩ (⌬t)2 ϩ 5t ϩ 5 ⌬t Ϫ t2 Ϫ 5t ϭ 2t ⌬t ϩ (⌬t)2 ϩ 5 ⌬t ϭ 2(3)(2) ϩ (2)2 ϩ 5(2) ϭ 26 feet B. vav ϭ ⌬y/⌬t ϭ 26/2 ϭ 13 feet per second C. vinst ϭ lim ⌬t S 0 f(t ϩ ⌬t) Ϫ f(t) 2t ⌬t ϩ (⌬t)2 ϩ 5 ⌬t ϭ lim ⌬t S 0 ⌬t ⌬t ϭ lim (2t ϩ ⌬t ϩ 5) ϭ 2t ϩ 5 ⌬t S 0 At t ϭ 5, vinst ϭ 2t ϩ 5 ϭ 2(5) ϩ 5 ϭ 15 feet per second. NOTE 1 Usually ⌬t is very small when compared to t. 27 28 BOB MILLER’S HIGH SCHOOL CALCULUS FOR THE CLUELESS NOTE 2 The derivative does not always exist.
The derivative of f(x), at a point x denoted b, fЈ(x), or dy/dx, is defined as f(x ϩ ⌬x) Ϫ f(x) ⌬x S 0 ⌬x lim if it exists. NOTE 1 All mathematics originally came from a picture. The idea of derivative came from the slope. Now the definition is independent of the picture. 25 26 BOB MILLER’S HIGH SCHOOL CALCULUS FOR THE CLUELESS NOTE 2 If y ϭ f(t) is a distance as a function of time t, then lim ⌬t S 0 f(t ϩ ⌬t) Ϫ f(t) ϭ fr(t) ⌬t is the velocity v(t). NOTE 3 In most books today, the notation is lim hS0 f(x ϩ h) Ϫ f(x) ϭ fr(x) h The letter h is used instead of ⌬x, ⌬y, or ⌬, whatever.
If the secant lines on each side approach one line, we say that this line is tangent to the curve at point P. We would like to develop the idea of tangent algebraically. We will review the development of slope from algebra. Given points P1—coordinates (x1, y1)—and P2— coordinates (x2, y2)—draw the line segment through P1 parallel to the x axis and the line segment through P2 parallel to the y axis, meeting at point Q. Since everything on P1Q has same y value, the y coordinate of Q is y1. Everything on P2Q has the same x value.