The accompanying figure shows a slope field for the differential equation y ′ = − x / y . (a) Use the slope field to estimate y 1 2 for the solution that satisfies the given initial condition y 0 = 1. (b) Compare your estimate to the exact value of y 1 2 .
The accompanying figure shows a slope field for the differential equation y ′ = − x / y . (a) Use the slope field to estimate y 1 2 for the solution that satisfies the given initial condition y 0 = 1. (b) Compare your estimate to the exact value of y 1 2 .
The accompanying figure shows a slope field for the differential equation
y
′
=
−
x
/
y
.
(a) Use the slope field to estimate
y
1
2
for the solution that satisfies the given initial condition
y
0
=
1.
(b) Compare your estimate to the exact value of
y
1
2
.
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.
3) If a is a positive number, what is the value of the following double integral?
2a
Love Lv
2ay-y²
.x2 + y2 dady
16. Solve each of the following equations for x.
(a) 42x+1 = 64
(b) 27-3815
(c) 92. 27² = 3-1
(d) log x + log(x - 21) = 2
(e) 3 = 14
(f) 2x+1 = 51-2x
11. Find the composition fog and gof for the following functions.
2
(a) f(x) = 2x+5, g(x) = x²
2
(b) f(x) = x²+x, g(x) = √√x
1
(c) f(x) = -1/2)
9
9(x) =
х
=
-
X
University Calculus: Early Transcendentals (4th Edition)
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