The ultimate test help an idiot learn calculus

[Fri]

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?

 

[Ray Vickson]

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?

What is S(z)? What do you get when you substitute z = P(y) into S(z)?

 

[SammyS]

...

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 other one step by step so maybe I can under stand it?

S(P(y) = (P(y))² .

P(y) = 2^y .

Combine those !

 

[epenguin]

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.