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The ultimate test! help an idiot learn calculus

  1. Jan 14, 2014 #1

    Fri

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    Hey I've been lurking on this forum all day trying to find answers / help to problems I can't solve in my calculus text. So I finally got the bright idea to make an account and ask questions :)

    Although first I want to mention that I'm very rusty in math so I may need the special step by step for dummies aid :p

    Ok I'm the beginning chapters of this textbook so this will mostly be easy stuff that I'm having trouble completing

    The problem is:

    Let S(x) = X^2, Let P(x) = 2^x, let s(x) = sin x. Find each of the following. In each case your answer should be a number.

    these are the two parts I need help on

    i) (S o P)(y)
    iii) (S o P o s)(t) + (s o P)(t)

    For (S o P)(y) I know:

    (S o P)(y) = S(P(y) = S(2^x(y)) = x^2(2^x(y)), but on the back of the book the answer is 2^2y I'm not sure how the author derived this answer. could someone maybe explain this and the otherone step by step so maybe I can under stand it?
     
  2. jcsd
  3. Jan 14, 2014 #2

    Ray Vickson

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    What is S(z)? What do you get when you substitute z = P(y) into S(z)?
     
  4. Jan 14, 2014 #3

    SammyS

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    S(P(y) = (P(y))2 .

    P(y) = 2y .

    Combine those !
     
  5. Jan 14, 2014 #4

    epenguin

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    The o in (S o P) signifies do operation S on P. S(x) = x^2 defines the operation S, It says square the thing (x, whatever x is) that S operates on. Whether that thing is a quantity, or another operation. S(x) = x^2, so S o P(y) is P(y)^2. (OK there is a trouble here, they are using two different notations for operations but you seem to have seen though that.)

    Your S(P(y)) = S(2^x(y)) = x^2(2^x(y)) is wrong or confused – the operators are operating on something which does not contain x, so x should ever appear at any point in the calculation.

    P(y)^2 is by rigid carrying over of the formula definition of P, (2^y)^2.
    To see how the result follows you may need to revise algebra of indices.
     
    Last edited: Jan 15, 2014
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