Recent content by navalava

Since light intensity increases with the number of photons, and the photon can be viewed as energy, would energy be proportional to intensity of light? Also since energy is inversely proportional to the wavelength of light, this would mean that the intensity of light is also inversely...

Ohh okay, that would make sense if the differential gives only the upper bound and not the absolute maximum error. But in that case is the differential considered reliable to give the actual maximum error? I'm pretty sure that they are used in practical applications as well, not just...

Homework Statement Four positive numbers, each less than 40, are rounded to the first decimal place and then multiplied together. Use differentials to estimate the maximum possible error in the computed product that might result from the rounding. Homework Equations...

Yeah, I differentiated it and got r'(1)=<0.841,0,0> and |r'(1)|=0.841, which seems like an odd number...I wanted to confirm that I did it right. I also got r2'(1)=<1,0,4> and |r2'(1)|=sq.root17. Is this right? And I just set them over each other to get the tangent vector right?

Homework Statement Consider the two space curves r1(t) = <cos(t − 1), t^2 − 1, 2t^4> r2(s) = <1 + ln s, s^2 − 2s + 1, 2s^2>, where t and s are two independent real parameters. Find the cosine of the angle between the tangent vectors of the two curves at the intersection point (1, 0, 2)...

Thank you! I see what I did wrong in substitution now!

Homework Statement Find an equation of the plane that contains these lines: r=<1,1,0>+t<1,-1,2> r=<2,0,2>+s<-1,1,0> Homework Equations The Attempt at a Solution I took the cross product of <1,-1,2> and <-1,1,0> to get <-2,-2,0>. I used the point (1,1,0) to get the equation of the...

Homework Statement Find an equation of the plane that passes through the point (6,0,-2) and contains the line x=4-2t, y=3+5t, z=7+4t. Homework Equations The Attempt at a Solution Here's what I did: I substituted t=2 to get: x=0, y=17, z= 15 So in total, we have three points...

Homework Statement Describe and sketch the surface in R^3: yz=4 Homework Equations The Attempt at a Solution So y= 4/z and z=4/y, and in 3-d that becomes two hyperboloids of one sheet...how do i connect them and what is the resulting figure called? I really appreciate the help!