Sorry I meant (1+x/n) = e^x is the same as your work?

I'm sorry, but I don't understand this run-on of incomplete sentences.

if so what about the (1+1/n) = e?

I'm sorry, but I don't understand what you are saying. Yes, the two different expressions stand for the two different values. How do you feel this to be incorrect?

Checking my math on the rectangle problem:

V(x)=x(20-2x)^2

=4x^3-80x^2+400x

V'(x)=12^2-160x+400

This should read "V'(x) = 12x^2 - 160x + 400".

4(x-10)(3x-10)=0

3x-10=0

3x=10

x=10/3

x=3.33

Leave this answer in exact form, rather than introducing round-off errors. Your instructor may also require that you check the other solution, confirming it to be invalid within context.

I also have another question as well: Find an equation of the tangent line of f(x) = sin^2(x) at 1/2

Here is what I got so far:

sin'x(sinx)+(sinx)sin'x

What is this? How does it relate to f(x) = (sin(x))^2?

=cosxsinx+sinxcosx

=2sinxcosx = sin2x = sin2(1/2) = sin(1)

Do not differentiate and evaluate at the same time. Do one, and only then do the other.

y = sin^2(sin)

What is this?

there is where I get stuck. I know I have to solve to find y1 and then plug it in y-y1 = sin(x+1/2).

What is "y1"? How does it relate to either of "f(x)" or "y"? What is the source of "sin(x + 1/2)"?

My supposition is that you are attempting to do two or three different things at once, and the resulting confusion is causing you to lose track of your progress and/or goal. Tis better to proceed methodically.

Before beginning, however, one must first determine the meaning of "at 1/2". Is this the value of x or of y? If not specified, kindly please consult with your instructor. Thank you.