Homework Statement
∫ Sinx cos x dx
Homework Equations
The Attempt at a Solution
If you integrate it using substitution, you get -cos2(x)/2but if you use double angle formula to rewrite the problem, it will be ∫1/2 sin(2x), and integrate it, you get -cos(2x)/4. isn't it weird?
Homework Statement
A rectangle has its base on the x-axis and its vertices on the positive portion of the parabola
$$ y=2-3x^2 $$
What is the maximum possible area of this rectangle?
A. (8/27)*181/2 B.(2/9)*181/2 C. (4/15)*301/2...
$$\lim_{x \to 0} \frac{4\sin^2(2x)}{x^2}$$
How do you use that limit to get 16?
This question comes from the AP test. So if I were to use the way I did to solve it , it would waste lots of time.
Homework Statement
The function f(x)=5x2+3e2x is invertible. Give the slope of the normal line to the graph of f-1 at x=3
Homework Equations
(f-1)'(x)=1/f'(f-1(x))
The slope of the normal line × the slope of the tangent =-1
So basically I just need to find -f'(f-1(x)) at x=3
The Attempt at a...
Okay. Here is how I tried.
Lim (4*(sin x)2)/x2 because no much difference between 2/t and 1/t
X→0
Then I got an indeterminant form 0/0, so I used L'hopital's rule.
Lim (8sin x cos x)/(2x)
X→0
Still 0/0 ,so again
Lim (8(cosx)2-8(sinx)2)/2
X→0
Which equals 4.
But my calculator says...