- 12.1: A contour map is shown for a function on the square . Use a Riemann...
- 12.2: Use the Midpoint Rule to estimate the integral in Exercise 1
- 12.3: Calculate the iterated integral.
- 12.4: Calculate the iterated integral.
- 12.5: Calculate the iterated integral.
- 12.6: Calculate the iterated integral.
- 12.7: Calculate the iterated integral.
- 12.8: Calculate the iterated integral.
- 12.9: Write as an iterated integral, where is the region shown and is an ...
- 12.10: Write as an iterated integral, where is the region shown and is an ...
- 12.11: Describe the region whose area is given by the integral
- 12.12: Describe the solid whose volume is given by the integral and evalua...
- 12.13: Calculate the iterated integral by first reversing the order of int...
- 12.14: Calculate the iterated integral by first reversing the order of int...
- 12.15: Calculate the value of the multiple integral.
- 12.16: Calculate the value of the multiple integral.
- 12.17: Calculate the value of the multiple integral.
- 12.18: Calculate the value of the multiple integral.
- 12.19: Calculate the value of the multiple integral.
- 12.20: Calculate the value of the multiple integral.
- 12.21: Calculate the value of the multiple integral.
- 12.22: Calculate the value of the multiple integral.
- 12.23: Calculate the value of the multiple integral.
- 12.24: Calculate the value of the multiple integral.
- 12.25: Calculate the value of the multiple integral.
- 12.26: Calculate the value of the multiple integral.
- 12.27: Calculate the value of the multiple integral.
- 12.28: Calculate the value of the multiple integral.
- 12.29: Find the volume of the given solid.Under the paraboloid and above t...
- 12.30: Find the volume of the given solid.. Under the surface and above th...
- 12.31: Find the volume of the given solid.The solid tetrahedron with vertices
- 12.32: Find the volume of the given solid.Bounded by the cylinder and the ...
- 12.33: Find the volume of the given solid.One of the wedges cut from the c...
- 12.34: Find the volume of the given solid.Above the paraboloid and below t...
- 12.35: Consider a lamina that occupies the region bounded by the parabola ...
- 12.36: A lamina occupies the part of the disk that lies in the first quadr...
- 12.37: (a) Find the centroid of a right circular cone with height and base...
- 12.38: Find the center of mass of the solid tetrahedron with vertices , , ...
- 12.39: The cylindrical coordinates of a point are . Find the rectangular a...
- 12.40: The rectangular coordinates of a point are . Find the cylindrical a...
- 12.41: The spherical coordinates of a point are . Find the rectangular and...
- 12.42: . Identify the surfaces whose equations are given.
- 12.43: Write the equation in cylindrical coordinates and in spherical coor...
- 12.44: Sketch the solid consisting of all points with spherical coordinate...
- 12.45: Use polar coordinates to evaluate
- 12.46: Use spherical coordinates to evaluate
- 12.47: Rewrite the integral as an iterated integral in the orde
- 12.48: Give five other iterated integrals that are equal to
- 12.49: Use the transformation , to evaluate , where is the square with ver...
- 12.50: Use the transformation , , to find the volume of the region bounded...
- 12.51: Use the change of variables formula and an appropriate transformati...
- 12.52: (a) Evaluate , where is an integer and is the region bounded by the...
Solutions for Chapter 12: Essential Calculus 2nd Edition
Full solutions for Essential Calculus | 2nd Edition
ISBN: 9781133112297
Solutions for Chapter 12
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Chapter 12 includes 52 full step-by-step solutions. Essential Calculus was written by and is associated to the ISBN: 9781133112297. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Essential Calculus, edition: 2. Since 52 problems in chapter 12 have been answered, more than 4929 students have viewed full step-by-step solutions from this chapter.
Key Calculus Terms and definitions covered in this textbook
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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.
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Ambiguous case
The case in which two sides and a nonincluded angle can determine two different triangles
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Angle
Union of two rays with a common endpoint (the vertex). The beginning ray (the initial side) can be rotated about its endpoint to obtain the final position (the terminal side)
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Census
An observational study that gathers data from an entire population
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Compound fraction
A fractional expression in which the numerator or denominator may contain fractions
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Dihedral angle
An angle formed by two intersecting planes,
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Even function
A function whose graph is symmetric about the y-axis for all x in the domain of ƒ.
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Exponential growth function
Growth modeled by ƒ(x) = a ? b a > 0, b > 1 .
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Factored form
The left side of u(v + w) = uv + uw.
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Identity function
The function ƒ(x) = x.
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Inverse secant function
The function y = sec-1 x
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Periodic function
A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.
-
Recursively defined sequence
A sequence defined by giving the first term (or the first few terms) along with a procedure for finding the subsequent terms.
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Response variable
A variable that is affected by an explanatory variable.
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Richter scale
A logarithmic scale used in measuring the intensity of an earthquake.
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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.
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Sinusoidal regression
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data
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Tangent
The function y = tan x
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x-coordinate
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.
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Zero of a function
A value in the domain of a function that makes the function value zero.