Bob Miller's High School Calc for the Clueless - Honors and by By (author) Bob Miller

By By (author) Bob Miller

With Bob Miller at your facet, you by no means need to be clueless approximately math back!

Algebra and calculus are difficult on highschool scholars such as you. Professor Bob Miller, with greater than 30 years' instructing event, is a grasp at making the advanced uncomplicated, and his now-classic sequence of Clueless learn aids has helped tens of millions comprehend the cruel subjects.

Calculus-with its integrals and derivatives-is well-known for tripping up even the fastest minds. Now Bob Miller-with his 30-plus years' event educating it-presents highschool calculus in a transparent, funny, and fascinating way.

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Extra info for Bob Miller's High School Calc for the Clueless - Honors and AP Calculus AB & BC

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A. Take point P on the curve. B. Take point Q1 on the curve. C. Draw PQ1. D. Take Q2, Q3, Q4, . . , drawing PQ2, PQ3, PQ4, . . with Qs approaching P. 23 Copyright © 2008 by The McGraw-Hill Companies, Inc. Click here for terms of use. 24 BOB MILLER’S HIGH SCHOOL CALCULUS FOR THE CLUELESS E. Do the same thing on the other side of P: Take R1, R2, . . such that R1 and R2 are approaching P. F. If the secant lines on each side approach one line, we say that this line is tangent to the curve at point P.

If you took the distance traveled and divided it by the time, you got the rate. The only difference is that in algebra, the average velocity was always the same. NOTE 2 Even if you drive a car at 30 mph, at any instant you might be going a little faster or slower. This is the instantaneous velocity. EXAMPLE 2— Let f(t) ϭ t2 ϩ 5t, with f(t) in feet and t in seconds. A. Find the distance traveled between the third and fifth seconds. B. Find the average velocity for 3 р t р 5. C. Find the instantaneous velocity at t ϭ 5.

In addition, f(3) ϭ 3. The function is continuous at x ϭ 3. ) At x ϭ 6, the limit as x goes to 6 from the left is 0. The limit as x goes to 6 from the right is 4. Since the two are different, the limit does not exist. The function is not continuous at 6 (see the jump). We do not have to test the second part of the definition since part 1 fails. EXAMPLE 23— Suppose 2x fsxd ϭ • ax ϩ b x3 xϽ1 1рxр4 xϾ4 If a and b are numbers to make f(x) continuous, we must find a and b. If x is continuous at x ϭ 1, limϪ2x ϭ limϩ(ax ϩ b).

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