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Math
Calculus
CALCULUS,EARLY TRANSCENDENTALS-ACCESS
Chapter 13.3, Problem 40E
Chapter 13.3, Problem 40E
BUY
CALCULUS,EARLY TRANSCENDENTALS-ACCESS
9th Edition
ISBN:
9780357128947
Author: Stewart
Publisher:
CENGAGE L
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1 Functions And Models
2 Limits And Derivatives
3 Differentiation Rules
4 Applications Of Differentiation
5 Integrals
6 Applications Of Integration
7 Techniques Of Integration
8 Further Applications Of Integration
9 Differential Equations
10 Parametric Equations And Polar Coordinates
11 Sequences, Series, And Power Series
12 Vectors And The Geometry Of Space
13 Vector Functions
14 Partial Derivatives
15 Multiple Integrals
16 Vector Calculus
A Numbers, Inequalities, And Absolute Values
B Coordinate Geometry And Lines
C Graphs Of Second-degree Equations
D Trigonometry
E Sigma Notation
F Proofs Of Theorems
G The Logarithm Defined As An Integral
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13.1 Vector Functions And Space Curves
13.2 Derivatives And Integrals Of Vector Functions
13.3 Arc Length And Curvature
13.4 Motion In Space: Velocity And Acceleration
Chapter Questions
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Problem 1E: (a) Use Equation 2 to compute the length of the given line segment. (b) Compute the length using the...
Problem 2E
Problem 3E: Find the length of the curve. 1. r(t) =t, 3 cos t, 3 sin t, 5 t 5
Problem 4E: Find the length of the curve. 2. r(t)=2t,t2,13t3, 0 t 1
Problem 5E: Find the length of the curve. 3. r(t)=2ti+etj+etk, 0 t 1
Problem 6E: Find the length of the curve. 4. r(t) =cos t i + sin t j +ln cos t k, 0 t /4
Problem 7E: Find the length of the curve. 5. r(t) = i + t2 j + t3 k, 0 t 1
Problem 8E: Find the length of the curve. 6. r(t) = t2 i + 9t j + 4t3/2 k, 1 t 4
Problem 9E: Find the length of the curve correct to four decimal places. (Use a calculator or computer to...
Problem 10E: Find the length of the curve correct to four decimal places. (Use a calculator or computer to...
Problem 11E: Find the length of the curve correct to four decimal places. (Use a calculator or computer to...
Problem 12E: Graph the curve with parametric equations x = sin t, y = sin 2t, z = sin 3t. Find the total length...
Problem 13E: Let C be the curve of intersection of the parabolic cylinder x2 = 2y and the surface 3z = xy. Find...
Problem 14E: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 +...
Problem 15E
Problem 16E
Problem 17E: Suppose you start at the point (0, 0. 3) and move 5 units along the curve x = 3 sin t, y = 4t, z = 3...
Problem 18E: Reparametrize the curve r(t)=(2t2+11)i+2tt2+1j with respect to arc length measured from the point...
Problem 19E: (a) Find the unit tangent and unit normal vectors T(t) and N(t) . (b) Use Formula 9 to find the...
Problem 20E: (a) Find the unit tangent and unit normal vectors T(t) and N(t) . (b) Use Formula 9 to find the...
Problem 21E: (a) Find the unit tangent and unit normal vectors T(t) and N(t) . (b) Use Formula 9 to find the...
Problem 22E: (a) Find the unit tangent and unit normal vectors T(t) and N(t) . (b) Use Formula 9 to find the...
Problem 23E: (a) Find the unit tangent and unit normal vectors T(t) and N(t). (b) Use Formula 9 to find the...
Problem 24E: (a) Find the unit tangent and unit normal vectors T(t) and N(t). (b) Use Formula 9 to find the...
Problem 25E: Use Theorem 10 to find the curvature. 21. r(t) = t3 j + t2 k
Problem 26E: Use Theorem 10 to find the curvature. 22. r(t) = t i = t2 j + et k
Problem 27E: Use Theorem 10 to find the curvature. 23. r(t)=6t2i+2tj+2t3k
Problem 28E
Problem 29E: Find the curvature of r(t) = t, t2, t3 at the point (1, 1, 1).
Problem 30E: Graph the curve with parametric equations x = cos t, y = sin t, z = sin 5t and find the curvature at...
Problem 31E: Use Formula 11 to find the curvature. 27. y = x4 28. y = tan x 29. y = xex
Problem 32E: To find: The curvature of y=tanx using Formula 11. Solution: The curvature of y=tanx is...
Problem 33E: Use Formula 11 to find the curvature. 27. y = x4 28. y = tan x 29. y = xex
Problem 34E: At what point does the curve have maximum curvature? What happens to the curvature as x ? 30. y =...
Problem 35E: At what point does the curve have maximum curvature? What happens to the curvature as x ? 30. y =...
Problem 36E: Find an equation of a parabola that has curvature 4 at the origin.
Problem 37E: (a) Is the curvature of the curve C shown in the figure greater at P or at Q? Explain. (b) Estimate...
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E: Curvature of Plane Parametric Curves The curvature of a plane parametric curve x=f(t),y=g(t) is...
Problem 48E: Curvature of Plane Parametric Curves The curvature of a plane parametric curve x=f(t),y=g(t) is...
Problem 49E
Problem 50E: Consider the curvature at x = 0 for each member of the family of functions f(x) = ecx. For which...
Problem 51E
Problem 52E
Problem 53E: Find equations of the normal plane and osculating plane of the curve at the given point. 49. x = sin...
Problem 54E: Find equations of the normal plane and osculating plane of the curve at the given point. 50. x = ln...
Problem 55E: Find equations of the osculating circles of the ellipse 9x2+4y2=36 at the points (2,0) and (0,3) ....
Problem 56E
Problem 57E: At what point on the curve x = t3, y = 3t, z = t4 is the normal plane parallel to the plane 6x + 6y ...
Problem 58E
Problem 59E: Find equations of the normal and osculating planes of the curve of intersection of the parabolic...
Problem 60E
Problem 61E
Problem 62E
Problem 63E: Show that the curvature is related to the tangent and normal vectors by the equation dTds=N
Problem 64E
Problem 65E
Problem 66E
Problem 67E: Use Formula 14 to find the torsion at the given value of t . 67. r(t)=12t2,2t,t,t=1
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E: Frenet-Serret Formulas The following formulas, called the Frenet-Serret formulas, are of fundamental...
Problem 73E: Show that the circular helix r(t)=acost,asint,bt , where a and b are positive constants, has...
Problem 74E: Find the curvature and torsion of the curve x = sinh t. y = cosh t, z = t at the point (0, 1, 0).
Problem 75E
Problem 76E
Problem 77E: The DNA molecule has the shape of a double helix (see Figure 13.1.3). The radius of each helix is...
Problem 78E
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