2. (a) Recall that or a parametric curve x = = f(t), y = g(t), where f, g are continuously differentiable, we have: dy = dx h(t) = g'(t) f'(t) where h is a function of the parameter t. Find h(t) for the parametric equations in Q1(a). d'y dz dx² dx' (b) Following *, write down a similar formula for the second derivative d'y where z = h(t). Hence compute as a function of t for the parametric equations in Q1(a). dx² -
2. (a) Recall that or a parametric curve x = = f(t), y = g(t), where f, g are continuously differentiable, we have: dy = dx h(t) = g'(t) f'(t) where h is a function of the parameter t. Find h(t) for the parametric equations in Q1(a). d'y dz dx² dx' (b) Following *, write down a similar formula for the second derivative d'y where z = h(t). Hence compute as a function of t for the parametric equations in Q1(a). dx² -
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please do the following question handwritten. Also attached is question 1a as it is asked in the main question, which is question 2
Transcribed Image Text:1. By eliminating the parameter t from the following parametric equations, find an equa-
tion in terms of x and y only whose graph is the same as the parametric curve. In each
case, decide if there are are any restrictions on the x and y coordinates.
(a) x = t³ + t,
(b)x=t, y = √t, (t = R).
(c) x = cos 2t, y =
=
Y t + 2, (t ≤ R).
cos² t, (0 ≤ t ≤ π).
Transcribed Image Text:2. (a) Recall that or a parametric curve x = f(t), y = g(t), where f, g are continuously
differentiable, we have:
h(t) =
dy
g' (t)
dx f'(t)
-
where h is a function of the parameter t. Find h(t) for the parametric equations
in Q1(a).
d²y dz
dx² dx'
(b) Following *, write down a similar formula for the second derivative
ď²y
where z = h(t). Hence compute as a function of t for the parametric equations
in Q1(a).
dx²
=
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