In Exercises 1−6, ( a ) express dw / dt as a function of t , both by using the Chain Rule and by expressing w in terms of t and differentiating directly with respect to t. Then ( b ) evaluate dw / dt at the given value of t . 2. w = x 2 + y 2 , x = cos t + sin t , y = cos t − sin t ; t = 0
In Exercises 1−6, ( a ) express dw / dt as a function of t , both by using the Chain Rule and by expressing w in terms of t and differentiating directly with respect to t. Then ( b ) evaluate dw / dt at the given value of t . 2. w = x 2 + y 2 , x = cos t + sin t , y = cos t − sin t ; t = 0
In Exercises 1−6, (a) express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t and differentiating directly with respect to t. Then (b) evaluate dw/dt at the given value of t.
2.
w
=
x
2
+
y
2
,
x
=
cos
t
+
sin
t
,
y
=
cos
t
−
sin
t
;
t
=
0
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
Which of the following pair of functions is linearly independent?
(a) ex, e(x-3)
(b) 4, sin2x+ cos?x
(c) 2sin2x, sinxcosx
) sinhx, (e-e)
Select one:
O a
Oc
O b
Let f = -2x² + 5y² where x = cos(t) and y = sin(t).
af
using the chain rule. Write your answer as a function of t.
Ət
Calculate
af
Ət
=
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Determine whether the functions fi(x) = cos 3r, f2(x) = x, and f3(r) = cos² r are linearly
independent on the interval (-x, 0).
Chapter 13 Solutions
University Calculus: Early Transcendentals (4th Edition)
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