I am not sure what I am doing wrong, but I just got this whole test wrong except one question.
Anyways I was having trouble with
1) Find the intervals on which $f(x)=x-2\cos x$, $0\leq x \leq 2\pi$,
- a) is increasing;
- b) decreasing.
I got $(\pi/6,\infty)$ increasing and $(-\infty, 0)$ decreasing. This is of course wrong but I don't quite understand what I was supposed to do differently. I forgot radians and had to figure it all out by hand because I don't have the unit circle memorized, this probably took me about half the test time (maybe an hour).
3) For the function $f(x) = (x+1)/x$, where is the graph
- a) concave up
- b) concave down
I got $0$ and $4$. I know this is wrong but I don't really know where I went wrong. I found the derivative and critical numbers $(2-x)/x^2$ and then I found the critical numbers, $-2$ then I found the derivative of that and got a critical number of $0$ and $4$ and found it was concave up on zero to $4$ and that is it.
7) Find the limit of $(\sec x-\tan x)$ as $x$ approached $\pi/2$.
I worked out $1/\cos x - \sin x/\cos x$ then $(1-\sin x)/\cos x$ and then $-\cos x/-\sin x = 0$.
I could pretty much post the entire test on here but I don't want to waste anyone's time.