1)
use the rule sin(a+b) = sin(a)cos(b)+cos(a)sin(b)


2. (3x-4)/(x^2+1)
quotient rule

(3(x^2+1) - 2x(3x-4))/ (x^2+1)^2
= (3x^2 + 3 - 6x^2 + 8x) / (x^2 +1)^2
= (-3x^2 +8x + 3) / (x^2+1)^2
a) (-3x^2 + 8x + 3) / (x^2 + 1)^2

b ) set that = to 0
(-3x^2 + 8x + 3) / (x^2 + 1)^2 = 0
(-3x^2 + 8x + 3) = 0
factorize it
(3x +1) (-x + 3) = 0
x = -1/3, 3

c)
make a sign chart and you will find that min at x =-1/3 because there is a sign change from negative to positive, and a max at 3 because there is a sign change from positive to negative. The two points are (-1/3, -45/10) min and (3, 1/2) as your max

This post was edited by lolcatslol on Nov 10 2013 10:14pm

for the first you can always write out the actual equation for sinh and cosh and compute

could use some help doing this problem
been busy moving since friday afternoon..

1. Prove the identity: sinh2x = 2sinhxcoshx

Done with all of the problems listed above. 1 Question left below with my work shown. Please lmk ASAP if my work is correct


Problem -----> Find the linearization of: y=sinhx at x=0

linear approximation = f(a) + f'(a)(x-a)

d/dx sinhx = coshx

f(0) = 0

f'(0) = 1

By plugging those into the linear approx formula we get:
f(0) + f'(0)(x-0)
0 + 1(x-0)
1x
x <--------------------- answer is x


Edit: sry i couldnt edit my above post.. i dont want any1 wasting time on a prob i have done already

This post was edited by CamelFinger on Nov 11 2013 02:23pm