By By (author) Bob Miller
With Bob Miller at your facet, you by no means must be clueless approximately math back!
Algebra and calculus are difficult on highschool scholars such as you. Professor Bob Miller, with greater than 30 years' educating adventure, is a grasp at making the complicated easy, and his now-classic sequence of Clueless research aids has helped tens of millions 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 fascinating way.
Read Online or Download Bob Miller's High School Calc for the Clueless - Honors and AP Calculus AB & BC PDF
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This ebook is particularly priceless to me as a instructor. i take advantage of it to complement the textual content examples.
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Additional info for Bob Miller's High School Calc for the Clueless - Honors and AP Calculus AB & BC
G(x ϩ ⌬x) Ϫ g(x) 2x ϩ ⌬x Ϫ 2x ϭ ⌬x ⌬x ϭ ϭ ( 2x ϩ ⌬x Ϫ 2x) ( 2x ϩ ⌬x ϩ 2x) ⌬x ( 2x ϩ ⌬x ϩ 2x) (x ϩ ⌬x) Ϫ x (⌬x)( 2x ϩ ⌬x ϩ 2x) ϭ ⌬x (⌬x)( 2x ϩ ⌬x ϩ 2x) ϭ 1 2x ϩ ⌬x ϩ 2x gr(x) ϭ lim ⌬x S 0 ϭ 1 2x ϩ ⌬x ϩ 2x 1 1 ϭ 2x ϩ 2x 2 2x The Basics 31 We can’t keep using the definition of derivative. If we had a complicated function, it would take forever. We will list the rules, interpret them, and give examples. Proofs are found in most calculus books. RULE 1 If f(x) ϭ c, then fЈ(x) ϭ 0. The derivative of a constant is 0.
If y ϭ sin x, yЈϭ cos x. B. If y ϭ cos x, yЈ ϭ Ϫsin x. C. If y ϭ tan x, yЈ ϭ sec2 x. D. If y ϭ cot x, yЈ ϭ Ϫcsc2 x. E. If y ϭ sec x, yЈ ϭ tan x sec x. F. If y ϭ csc x, yЈ ϭ Ϫcot x csc x. Once you prove A, B is proved by using the identities cos x ϭ sin(/2 Ϫ x), sin x ϭ cos(/2 Ϫ x), and rule 9. Once A and B are proved, C through F are proved by writing those four in terms of sin x and cos x, by using rule 8 and other basic trig identities. However, I always like to prove that the derivative of the sine is the cosine.
The Basics NOTE 1 The average velocity is very similar to the rate you learned in elementary algebra. 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.