Particle MotionA particle moves in the yz-plane along the curve represented by the
(a) Describe the curve.
(b) Find the minimum and maximum values of
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Chapter 12 Solutions
WebAssign Printed Access Card for Larson/Edwards' Calculus, Multi-Term
- VelocitySuppose that in Exercise 55 the current is flowing at 1.2 mi/hr due south. In what direction should the swimmer head in order to arrive at a landing point due east of his starting point? VelocityA river flows due south at 3mi/h. A swimmer attempting to cross the river heads due east swimming at 2mi/h relative to the water. Find the true velocity of the swimmer as a vector.arrow_forwardshow solution in a paperarrow_forwardr'(to) TIr(to)|| A vector-valued function and its graph are given. The graph also shows the unit vectors r"(to) Find these two unit vectors and identify them and Ilr"(to)|| as a or b on the graph. r(t) = cos(nt)i + sin(nt)j + t²k, to %3D 4. r'(to) Tr(to)|| a/2i+V2j- k V 4n +1 r"(to) I|r"(to)|| V at + 4 %3D a varrow_forward
- Sketch and describe the curve defined by the vector-valued function below. 7(t) = (t cos t, t, t sin t), t > 0. Explain, in words, some properties of the curve as t gets bigger.arrow_forwardCurve C is any curvearrow_forward(1n |t – 1], e', vî ) 1. Let 7(t) = (a) Express the vector valued function in parametric form. (b) Find the domain of the function. (c) Find the first derivative of the function. (d) Find T(2). (e) Find the vector equation of the tangent line to the curve when t=2. 2. Complete all parts: (a) Find the equation of the curve of intersection of the surfaces y = x? and z = x3 (b) What is the name of the resulting curve of intersection? (c) Find the equation for B the unit binormal vector to the curve when t= 1. Hint: Instead of using the usual formula for B note that the unit binormal vector is orthogonal to 7 '(t) and 7"(t). In fact, an alternate formula for this vector is ア'(t) × ア"(t) ア(t) ×デ"(t)| B(t) =arrow_forward
- 3. Turn in: Find the equation for the tangent line to the curve defined by the vector-valued function: r(t)=(sint, 3e, e) at the point (1)- (0,3,1). You can express the equation in parametric or symmetric form.arrow_forwardCalculus IIIarrow_forwardQuestion described by the vector function r(t) = (4t² Int, -2e-3t). t-4 a) Find the integral ſ r(t)dt. b) Find parametric equations for the tangent line to the given curve at the point (0, -3, -2e-³). c) Consider the curve which is 29 Can you find parametric equations for the tangent line to the given curve at the point (0, -2,-2)?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning