Recent content by grapeape

Homework Statement A spherical aluminum ball of mass 1.48 kg contains an empty spherical cavity that is concentric with the ball. The ball just barely floats in water. A. Calculate the outer radius of the ball. B. Calculate the radius of the cavity Homework Equations Buoyant Force...

does y = x + cos x have any asymptotes? (horizontal or vertical) Vertical = none, the limit as x approaches infinity is infinity? And for negative infinity its negative infinity? is that possible since infinity is not in the domain of cos? or are there also no horizontal?

This is only part of my question and I need the answer to continue, when does cos x = -x? on my calculator it is -.7390... isn't it supposed to be a nicer number ie pi over something?

alright, thanks. I am pretty sure I got it now. I used IMVT to prove that between -2, and -1 there is another 0, and since there is only 1 critical number it is the only other 0 asides from (0,0). Seems right, thanks for the help Andy and Halls!

So, since there is only 1 critical point, how do we know that there aren't more? asides from using a graphing calculator. By looking at the first derivative and finding 1 root, does that automatically mean that there are two roots? I'm a little confused on how Rolle's theorem ties into this. Am...

the derivative is 4x^3 + 4, which has a zero at -1. But how do I eliminate the possibility of other zeroes? do I have to take the double deriv? and also how do I prove the f(x) has only 2 zeroes?

Homework Statement Show that f(x) = x^4 + 4x + c = 0 has at most 2 roots. Homework Equations The Attempt at a Solution I'm not really sure how to approach this problem, I think I have to use the IMVT / Rolle's Theorem / MVT. Any help to even get me started would be greatly...

I love this forum. Thanks for all the help!

so do I do ( -20cos(30)/sin(30)^2 ) x pi/180? if so I got -1.209. Can error be negative? Or since it's both +/- 1 degree, do you also do another equation multiplying by a negative pi/180. My real questions are, how is error represented (multiple numbers, one number, a continuum)? And, how do I...

Homework Statement One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30(degrees), with a possible error of +/- 1 degree. a) Use differentials to estimate the error in computing the length of the hypotenuse b) what is the percentage error...