a. Use the method of Exercise 7 to find N for the curve r(t) = t i
Question:
a. Use the method of Exercise 7 to find N for the curve r(t) = t i + (1/3)t3 j when t 0.
b. Calculate N for t ≠ 0 directly from T using Equation (4) for the curve in part (a). Does N exist at t = 0? Graph the curve and explain what is happening to N as t passes from negative to positive values.
Data from in Exercise 7
a. Show that n(t) = -g′(t)i + ƒ′(t)j and -n(t) = g′(t)i - ƒ′(t)j are both normal to the curve r(t) = ƒ(t)i + g(t)j at the point (ƒ(t), g(t)).
To obtain N for a particular plane curve, we can choose the one of n or -n from part (a) that points toward the concave side of the curve, and make it into a unit vector. (See Figure 13.19.) Apply this method to find N for the following curves.
In Figure 13.19
Step by Step Answer:
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir