Recent content by avr10

Thanks guys; I implicitly differentiated and found that \frac {dx}{dy} = \frac {15 - 32y}{18x + 44} . I used this to say that when the denominator is 0, namely when x is -44/18, x is an extreme. Does this sound right?

Thanks; the 120 was a typo which I now fixed. When I do that (I used \tan{\theta} = 150/y ), I end up getting something like 3000 ft/s, which I think there is something wrong with... why am I getting such a big number?

Homework Statement The parabola 9x^{2} + 24xy + 16y^{2} + 20x - 15y = 0 has vertex at the origin. Find the coordinates of the points on the parabola that have extreme x-values Homework Equations The Attempt at a Solution To start off, I don't quite understand the question...

Homework Statement You are 150 feet away from a road. Looking down the road, you notice a car heading in your direction such that the angle formed by your line of vision to the car and the road is 45 degrees, and this angle is increasing at a rate of 10 degrees per second. How fast is the...

Hm? Why is that?

Thanks, I integrated it successfully, but since this is a definite integral, at the end I'm not quite sure what to do with the boundaries, namely with the m term. Is it okay to leave the answer as an expression of both m and x? It comes out to this: \frac {1}{4} (x^{4} ln{x} - \int^m_1...

Homework Statement \text {Evaluate } \int^m_1 x^{3}ln{x}\,dx Homework Equations The Attempt at a Solution Integrating by parts, but not sure which term to substitute out...it's not turning out clean...argh I've done every other problem except for this one, can someone just...

Homework Statement A particle moves along the parabola y = 4x^{2} such that it's x coordinate increases at a steady rate of 5 units/minute. How fast is the particle's distance from the origin changing when it is at the point (1,4)? Homework Equations The Attempt at a Solution...

Thanks, in order to show that it is maximal at infinity, does it suffice to say that since x must always be greater than 0, then the integral is maximal at infinity? That doesn't sound very rigorous...how would you phrase it?

Homework Statement \text {Find m such that }\displaystyle\int^m_4 \frac{1}{x\sqrt{x}}\,dx = .9 Homework Equations The Attempt at a Solution \displaystyle\int^m_4 \frac{1}{x\sqrt{x}}\,dx = .9 \Rightarrow \displaystyle\int^m_4 x^{-3/2}\,dx = .9 \Rightarrow -2m^{-1/2}...

Homework Statement Hi all, I'm new here, and just have a quick question: Evalute: lim as x\rightarrow\infty of \frac{x - sin x}{x^{3}} Homework Equations l'hopital's rule? The Attempt at a Solution So far I've used L'hopital's rule to get it down to lim as x\rightarrow\infty...