Recent content by karens

Homework Statement Consider that f(x, y) = [sin^2(x − y)] / [|x| + |y|]. Using this, prove: lim(x,y)→(0,0) f(x, y) = 0 Homework Equations Definition of a limit, etc. The Attempt at a Solution I don't know how to start... I've been trying to self-teach limits for a while and...

nvmnd - solved

Homework Statement n. Let r1 and r2 be differentiable 3-space vector-valued functions. Directly from the definition of dot product, and the definition of derivative of vector- valued functions in terms of components, prove that d/dt (r1(t) • r2(t)) = r′1(t) • r2(t) + r1(t) • r′2(t). Homework...

Homework Statement Let r1 and r2 be differentiable 3-space vector-valued functions. Show that for a differentiable 3-space vector-valued function r, the graph of r lies on a sphere centered at the origin if and only if r(t) and r′(t) are orthogonal (perpendicular) for all t. Homework...

Homework Statement Prove that r1 and r2 intersect at (1,1,3). Let r1 and r2 be defined as: r1(t)=t^2i+tj+3t^3k r2(t)=(t−1)i+(1/4)t^2j+(5−t)k Homework Equations Intersection is derived from r1=r2. The Attempt at a Solution I only formally get to this point and then start...

What does the arc length parametrization mean?