- 5.5.1: A cup of coffee at 90C is put into a 20C room when t = 0. The coffe...
- 5.5.2: If the marginal cost function C(q) is measured in dollars per ton, ...
- 5.5.3: The marginal cost of drilling an oil well depends on the depth at w...
- 5.5.4: The population of Tokyo grew at the rate shown in Figure 5.65. Esti...
- 5.5.5: A marginal cost function C(q) is given in Figure 5.66. If the fixed...
- 5.5.6: Figure 5.67 shows the rate of change of the quantity of water in a ...
- 5.5.7: The total cost in dollars to produce q units of a product is C(q). ...
- 5.5.8: The marginal cost C(q) (in dollars per unit) of producing q units i...
- 5.5.9: The marginal cost function for a company is given by C(q) = q2 16q ...
- 5.5.10: The marginal cost function of producing q mountain bikes is C(q) = ...
- 5.5.11: The marginal revenue function on sales of q units of a product is R...
- 5.5.12: Figure 5.68 shows P(t), the rate of change of the price of stock in...
- 5.5.13: The net worth, f(t), of a company is growing at a rate of f(t) = 20...
- 5.5.14: The graph of a derivative f(x) is shown in Figure 5.69. Fill in the...
- 5.5.15: The derivative f(x) is graphed in Figure 5.70. Fill in the table of...
- 5.5.16: What does the value of =t0 0 r(t) dt tells us about the oil well?
- 5.5.17: Rank in order from least to greatest: < 2t0 0 r(t) dt, < 2t0 t0 r(t...
- 5.5.18: In 1820, let C(n) be a citys cost, in millions of dollars, for plow...
- 5.5.19: In 1820, let C(n) be a citys cost, in millions of dollars, for plow...
- 5.5.20: In 1820, let C(n) be a citys cost, in millions of dollars, for plow...
- 5.5.21: Which is larger: < 2 0 r(t) dt or < 4 2 r(t) dt?
- 5.5.22: Which is larger: < 4 0 r(t) dt or 4r(4)?
- 5.5.23: Give a reasonable overestimate of < 8 0 r(t) dt.
Solutions for Chapter 5.5: TOTAL CHANGE AND THE FUNDAMENTAL THEOREM OF CALCULUS
Full solutions for Applied Calculus | 5th Edition
A value ƒ(c) is an absolute maximum value of ƒ if ƒ(c) ? ƒ(x) for all x in the domain of ƒ.
Absolute value of a complex number
The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.
A set of points in a plane equally distant from a fixed point called the center
Trigonometric functions when applied to real numbers are circular functions
Component form of a vector
If a vector’s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x-, y-, and z-components of the vector, respectively)
For the equation ax 2 + bx + c, the expression b2 - 4ac; for the equation Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, the expression B2 - 4AC
The behavior of a graph of a function as.
Matrices that have the same order and equal corresponding elements.
The difference between the third quartile and the first quartile.
Limit at infinity
limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x:- q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large
Angle measure equal to 1/60 of a degree.
See Periodic function.
Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2
Any one of the four parts into which a plane is divided by the perpendicular coordinate axes.
Quotient rule of logarithms
logb a R S b = logb R - logb S, R > 0, S > 0
A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.
Standard position (angle)
An angle positioned on a rectangular coordinate system with its vertex at the origin and its initial side on the positive x-axis
Sum of functions
(ƒ + g)(x) = ƒ(x) + g(x)
Vertices of an ellipse
The points where the ellipse intersects its focal axis.
The directed distance from the y-axis yz-plane to a point in a plane (space), or the first number in an ordered pair (triple), pp. 12, 629.