solve part B
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
solve part B
Transcribed Image Text:a. Show that n(t) = -g'(t)i + f'(t)j and - n(t) = g'(t)i - f (t)j are both normal to the curve r(t) = f(t)i + g(t)j at the
point (f(t).g(t)).
To obtain N for a particular plane curve, choose the one of n or -n that points toward the concave side of the
curve, and make it into a unit vector. (See the figure to the right.) Apply this method to find N for the following
N-4.
P.
curves.
b. r(t) = 4ti + 4 j
Pot
c. (t) = /16 - 49t i+ 7tj, - sts
The vector dT/ds, normal to the curve, always points in the
direction in which T is turning. The unit normal vector
is the
direction of dT/ds
O A. Show that v•T= - 1.
O B. Show that n•v= - 1.
O C. Show that v•T=0.
YD. Show that n•v = 0.
Why is the equation from the previous step satisfied?
A. The components of n(t) are the components of v(t) with the order swapped and the sign of one changed, so the dot product is 0.
O B. The components of n(t) are negative reciprocals of the components of T, so the dot product is - 1.
OC. The components of n(t) are negative reciprocals of the components of v(t), so the dot product is - 1.
O D. The sum of the components of v(t) is the negative of T, so the dot product is 0.
b. N= ( Di+
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