Reference no: EM131012444
1. Arc Length:
a. Consider the following vector function:
r (t) = (t, 2t2, 8/3t3)
i. Determine the direction and magnitude of the vector derivative at t = 1.
ii. Determine the length of the curve from 0 ≤ t ≤ 1.
b. Consider the following vector function:
r(t) = (et, e-t, √2t).
i. State the domain of r.
ii. Determine the direction and magnitude of the vector derivative at t = ln(2).
iii. Determine the length of the curve from 0 ≤ t ≤ 1.
c. Reparametrize the following curves by arc length, starting from t = 0:
i. r(t) = (l+2t, 5-t, 3t)
ii. r(t) = (sin (t), 2t, cos (t))
iii. r(t) = (e3t sin (3t), e3t cos (3t)).
2. Multivariate Functions:
a. Consider the following multivariate function:
f(x. y) = y/(x2- 1)
i. State the domain of f.
ii. Sketch the contour plot of f in the (x, y)-plane.
iii. Determine the direction and magnitude of steepest ascent at the point (0,2).
iv. Is the function continuous at the point (1. 0)? Justify your answer.
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