Find a change of parameter t = g τ for the semicircle r t = cos t i + sin t j 0 ≤ t ≤ π Such that (a) the semicircle is traced counterclockwise as τ varies over the interval 0 , 1 (b) the semicircle is traced clockwise as τ varies over the interval 0 , 1 .
Find a change of parameter t = g τ for the semicircle r t = cos t i + sin t j 0 ≤ t ≤ π Such that (a) the semicircle is traced counterclockwise as τ varies over the interval 0 , 1 (b) the semicircle is traced clockwise as τ varies over the interval 0 , 1 .
Consider the curve x = et-5 cos t, y = et-5 sin t, 0 < t < 2n.
a) Find the values of t where the line tangent to the curve is vertical.
b) Find the values of t where the slope of the line tangent to the curve is -1.
A sinusoidal curve y = a + b sin(cx) where a>0, b>0 and c>0, has 2 concurrent maximum points at
coordinates (60°, 5) and (300°, 5).Given that it also has an amplitude of 2 units, determine the values of a
and b and determine the least possible value of c.
f(x) = 5 sinx + 4 cos x, on (-π, π)
a) Determine the intervals on which f is concave up and concave down.
f is concave up on:
f is concave down on:
b) Based on your answer to part (a), determine the inflection points of f. Each point should be entere
an ordered pair (that is, in the form (x, y)).
(Separate multiple answers by commas.)
c) Find the critical numbers of f and use the Second Derivative Test, when possible, to determine the
relative extrema. List only the x-coordinates.
V
Relative maxima at:
(Separate multiple answers by commas.)
(Separate multiple answers by commas.)
Relative minima at:
d) Find the x-value(s) where f'(x) has a relative maximum or minimum.
f' has relative maxima at:
(3))
5
f' has relative minima at:
200
-tan
(Separate multiple answers by commas.)
(Separate multiple answers by commas.)
AR N
150
PAR JOURNE
ال التي ال ا
x
TO
1
T
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