MATH 2415-301 Exam II Review Problems 1. Find parametric equations for the tangent line to the curve with parametric e = t cos t, y = t, z = tsint; (T, T, 0) 2. Find the arc length of r(t) = i+tj + 2tk on 1, 2. 3. Find the arc lenght of one turn of the helix r(t) = (cos t) i + (sint)j+tk. particle that moves along the 4. Find the velocity, speed, and acceleration of a t t (t) (2 sin)i+(2 cos )j at t 2 5. Find the unit tangent and the principal unit normal vectors for the h (2 cos t) i+(2 sin t) j+tk. r(t) 6. Find the curvature of r(t) = ti+ t2j + t k. 7. Find the curvature of the plane y = cos(r) + e2 at r 0. 8. Find the maximum curvature of y In x. hac cunvedune, hec eluriv 9. Find the tangential component ar and normal component aN for the cu r(t) 3ti tj+tk. 10. Let a(t) 2t i + e'j+ cos (t) k denote the acceleration of a moving pa i+2j- k, find the particle's velocity v(t) at any time t. v(0) M (a) Find the domain of f(x, y) V2- In(-1) (b) Sketch the graph of f(x, y) =6-x-2y.

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Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.