EXERCISE 1.64. For the helix in Example 1.3, defined as y(t) (cost, sint,t), t E R, com defined as (t) (cos t, sin t,-t), te R. Describe the visual difference between a helix with positive torsio...
3. A shape is defined as: (x, y, z) = (rcos 0 sin 0,r sin sin d, r cos ø) with 0r1, T/4 < 0< 7t/4 and 0 < ¢ < T* 2 marks (a) Describe this region. an appropriate integration, determine the volume of this shape [4 marks (b) Using 3 (Continued) 3 marks (c) Parametrise the surface of this shape. 3 marks (d) Find a normal to the surface [4 marks (e) What is the surface area of...
EXAMPLE 1 (a) Find the derivative of r(t) = (3 + t4)1+ te-y + sin(40k. (b) Find the unit tangent vector at the point t0. SOLUTION (a) According to this theorem, we differentiate each component of r: t 45 cos (4t) r(t) + 3 (b) Since r(0)= and r(o) j+4k, the unit tangent vector at the point (3, 0, 0) is i+ 4k T(0) = L'(0)--
EXAMPLE 1 (a) Find the derivative of r(t) = (3 + t4)1+ te-y +...
#40 a-f
B-A. (B+A ". Beats slation Recall the identity cos A-cos Be2-2A)sin(-2A) a. Show that 0-10,a, . 9 and (ii)o_10,us2toverify the identity. In which case do you see Gaph the functions on both sides of the equation in part (a) with (i) beats? b. 40 Analysis of the forced damped oscillation equation Consider the equation my"+ey'+ky Fo cos wof, which oscillator. Assume all the parameters in the equation are positive. a. Explain why the solutions of the homogeneous equation...
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All of the following questions are in relation to the following journal article which is available on Moodle: Parr CL, Magnus MC, Karlstad O, Holvik K, Lund-Blix NA, Jaugen M, et al. Vitamin A and D intake in pregnancy, infant supplementation and asthma development: the Norwegian Mother and Child Cohort. Am J Clin Nutr 2018:107:789-798 QUESTIONS: 1. State one hypothesis the author's proposed in the manuscript. 2. There is previous research that shows that adequate Vitamin A intake is required...