Consider the curve x^3 + 4xy + y^2 = 6. Find the equation of the tangent line to the curve at the point (1, 1) in the form y = mx + b. Consider the curve x^4 + 3xy + y^5 = 5. Find the equation of the tangent line to ...
A circle in the xy-plane has a center at the origin and a radius of 3. Let f be a function defined on the closed interval -3 less than or equal to x less than or equal to 3? For each number b in the d Find the radius of the circle...
What is the geometric interpretation of this result? Find a vector function r(t) that parametrizes the curve y = x^2 - 4 in the xy-plane. Find the vectors T and N, and the unit binomial vector B = T \times N, for the vector-valued function r(...
Integrate f(x, y, z) = z over the ice cream cone-shaped region W, lying above the cone x^2 + y^2 = z^2 and below the sphere x^2 + y^2 + z^2 =1 . Let R be the region above the xy-plane bounded below...