- 8-6.Q1: If y = x3, then dL (arc length) = ?.
- 8-6.Q2: If y = tan x, then dL = ?.
- 8-6.Q3: sin5 x cos x dx = ?
- 8-6.Q4: ?
- 8-6.Q5: If y = x ex, then y = ?.
- 8-6.Q6: The maximum of y = x2 8x + 14 on the interval [1, 6] is ?
- 8-6.Q7: Write the definition of derivative.
- 8-6.Q8: Give the physical meaning of derivative.
- 8-6.Q9: sec 2x dx = ?
- 8-6.Q10: If lim Un = lim Ln for function f, then f is ?. A. Differentiable B...
- 8-6.1: Paraboloid Problem: A paraboloid is formed by rotating about the y-...
- 8-6.2: Rotated Sinusoid Problem: One arch of the graph of y = sin x is rot...
- 8-6.3: ln Curved Surface, I: The graph of y = ln x from x = 1 to x = 3 is ...
- 8-6.4: ln Curved Surface, II: The graph of y = ln x from x = 1 to x = 3 is...
- 8-6.5: Reciprocal Curved Surface I: The graph of y = 1/x from x = 0.5 to x...
- 8-6.6: Reciprocal Curved Surface II: The graph of y = 1/x from x = 0.5 to ...
- 8-6.7: Cubic Paraboloid I: The cubic paraboloid y = x3 from x = 0 to x = 2...
- 8-6.8: Cubic Paraboloid II: The part of the cubic parabola y = x3 + 5x2 8x...
- 8-6.9: For 916, write an integral equal to the area of the surface. Evalua...
- 8-6.10: For 916, write an integral equal to the area of the surface. Evalua...
- 8-6.11: For 916, write an integral equal to the area of the surface. Evalua...
- 8-6.12: For 916, write an integral equal to the area of the surface. Evalua...
- 8-6.13: For 916, write an integral equal to the area of the surface. Evalua...
- 8-6.14: For 916, write an integral equal to the area of the surface. Evalua...
- 8-6.15: For 916, write an integral equal to the area of the surface. Evalua...
- 8-6.16: For 916, write an integral equal to the area of the surface. Evalua...
- 8-6.17: 7. Sphere Zone Problem: The circle with equation x2 + y2 = 25 is ro...
- 8-6.18: Sphere Total Area Formula Problem: Prove that the surface area of a...
- 8-6.19: Sphere Volume and Surface Problem: You can find the volume of a sph...
- 8-6.20: Sphere Rate of Change of Volume Problem: Prove that the instantaneo...
- 8-6.21: Paraboloid Surface Area Problem: Figure 8-6k shows the paraboloid f...
- 8-6.22: Zone of a Paraboloid Problem: Zones of equal altitude on a sphere h...
- 8-6.23: Ellipsoid Problem: The ellipse with x-radius 5 and y-radius 3 and p...
- 8-6.24: Cooling Tower Problem: Cooling towers for some power plants are mad...
- 8-6.25: Lateral Area of a Cone Problem: Figure 8-6m shows a cone of radius ...
- 8-6.26: Lateral Area of a Frustum Problem: Figure 8-6n shows that a frustum...
Solutions for Chapter 8-6: Length of a Plane CurveArc Length
Full solutions for Calculus: Concepts and Applications | 2nd Edition
A combination of variables and constants involving addition, subtraction, multiplication, division, powers, and roots
The numbers in Pascal’s triangle: nCr = anrb = n!r!1n - r2!
The principle of experimental design that makes it possible to rule out other factors when making inferences about a particular explanatory variable
De Moivre’s theorem
(r(cos ? + i sin ?))n = r n (cos n? + i sin n?)
Variable representing the range value of a function (usually y)
A statement of equality between two expressions.
equation of an ellipse
(x - h2) a2 + (y - k)2 b2 = 1 or (y - k)2 a2 + (x - h)2 b2 = 1
Arrows that have the same magnitude and direction.
Equivalent equations (inequalities)
Equations (inequalities) that have the same solutions.
Horizontal shrink or stretch
See Shrink, stretch.
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.
A function viewed as a mapping of the elements of the domain onto the elements of the range
Multiplication property of inequality
If u < v and c > 0, then uc < vc. If u < and c < 0, then uc > vc
An annuity in which deposits are made at the same time interest is posted.
See Parametric equations.
A transformation that leaves the basic shape of a graph unchanged.
A plot of all the ordered pairs of a two-variable data set on a coordinate plane.
Shrink of factor c
A transformation of a graph obtained by multiplying all the x-coordinates (horizontal shrink) by the constant 1/c or all of the y-coordinates (vertical shrink) by the constant c, 0 < c < 1.
Standard form of a polar equation of a conic
r = ke 1 e cos ? or r = ke 1 e sin ? ,
An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.