Calculus: Single Variable, Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)
3rd Edition
ISBN: 9780134996714
Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher: PEARSON
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Chapter 6.1, Problem 18E
a.
To determine
The position function of the given velocity by anti-derivative method.
b.
To determine
The position function of the given velocity by Fundamental theorem of calculus.
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Chapter 6 Solutions
Calculus: Single Variable, Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)
Ch. 6.1 - A police officer leaves his station on a...Ch. 6.1 - Describe a possible motion of an object along a...Ch. 6.1 - Is the position s(t) a number or a function? For...Ch. 6.1 - Without doing further calculations, what are the...Ch. 6.1 - Prob. 5QCCh. 6.1 - Prob. 6QCCh. 6.1 - Explain the meaning of position, displacement, and...Ch. 6.1 - Suppose the velocity of an object moving along a...Ch. 6.1 - Given the velocity function v of an object moving...Ch. 6.1 - Prob. 4E
Ch. 6.1 - Prob. 5ECh. 6.1 - What is the result of integrating a population...Ch. 6.1 - Displacement and distance from velocity Consider...Ch. 6.1 - Displacement and distance from velocity Consider...Ch. 6.1 - Velocity graphs The figures show velocity...Ch. 6.1 - Prob. 10ECh. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Displacement from velocity Consider an object...Ch. 6.1 - Displacement from velocity Consider an object...Ch. 6.1 - Displacement from velocity Consider an object...Ch. 6.1 - Displacement from velocity Assume t is time...Ch. 6.1 - Position from velocity Consider an object moving...Ch. 6.1 - Prob. 18ECh. 6.1 - Position from velocity Consider an object moving...Ch. 6.1 - Prob. 20ECh. 6.1 - Prob. 21ECh. 6.1 - Prob. 22ECh. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Flying into a headwind The velocity (in mi/hr) of...Ch. 6.1 - Day hike The velocity (in mi/hr) of a hiker...Ch. 6.1 - Piecewise velocity The velocity of a (fast)...Ch. 6.1 - Probe speed A data collection probe is dropped...Ch. 6.1 - Position and velocity from acceleration Find the...Ch. 6.1 - Position and velocity from acceleration Find the...Ch. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.1 - Position and velocity from acceleration Find the...Ch. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.1 - Prob. 36ECh. 6.1 - Prob. 37ECh. 6.1 - Prob. 38ECh. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Prob. 41ECh. 6.1 - Prob. 42ECh. 6.1 - Population growth 43. A culture of bacteria in a...Ch. 6.1 - Prob. 44ECh. 6.1 - Oil production An oil refinery produces oil at a...Ch. 6.1 - Prob. 46ECh. 6.1 - Prob. 47ECh. 6.1 - Prob. 48ECh. 6.1 - Prob. 49ECh. 6.1 - Prob. 50ECh. 6.1 - Prob. 51ECh. 6.1 - Prob. 52ECh. 6.1 - Prob. 53ECh. 6.1 - Prob. 54ECh. 6.1 - Prob. 55ECh. 6.1 - Prob. 56ECh. 6.1 - Marginal cost Consider the following marginal cost...Ch. 6.1 - Prob. 58ECh. 6.1 - Explain why or why not Determine whether the...Ch. 6.1 - Prob. 60ECh. 6.1 - Prob. 61ECh. 6.1 - Prob. 62ECh. 6.1 - Prob. 63ECh. 6.1 - Prob. 64ECh. 6.1 - Prob. 65ECh. 6.1 - Prob. 66ECh. 6.1 - Prob. 67ECh. 6.1 - Variable gravity At Earths surface, the...Ch. 6.1 - Prob. 69ECh. 6.1 - Prob. 70ECh. 6.1 - Another look at the Fundamental Theorem 71. Use...Ch. 6.1 - Prob. 72ECh. 6.2 - In the area formula for a region between two...Ch. 6.2 - Prob. 2QCCh. 6.2 - Prob. 3QCCh. 6.2 - Prob. 4QCCh. 6.2 - Set up a sum of two integrals that equals the area...Ch. 6.2 - Set up an integral that equals the area of the...Ch. 6.2 - Make a sketch to show a case in which the area...Ch. 6.2 - Make a sketch to show a case in which the area...Ch. 6.2 - Find the area of the region (see figure) in two...Ch. 6.2 - Find the area of the region (see figure) in two...Ch. 6.2 - Express the area of the shaded region in Exercise...Ch. 6.2 - Prob. 8ECh. 6.2 - Finding area Determine the area of the shaded...Ch. 6.2 - Prob. 10ECh. 6.2 - Finding area Determine the area of the shaded...Ch. 6.2 - Prob. 12ECh. 6.2 - Finding area Determine the area of the shaded...Ch. 6.2 - Prob. 14ECh. 6.2 - Finding area Determine the area of the shaded...Ch. 6.2 - Prob. 16ECh. 6.2 - Finding area Determine the area of the shaded...Ch. 6.2 - Prob. 18ECh. 6.2 - Finding area Determine the area of the shaded...Ch. 6.2 - Finding area Determine the area of the shaded...Ch. 6.2 - Finding area Determine the area of the shaded...Ch. 6.2 - Prob. 22ECh. 6.2 - Finding area Determine the area of the shaded...Ch. 6.2 - Prob. 24ECh. 6.2 - Finding area Determine the area of the shaded...Ch. 6.2 - Prob. 26ECh. 6.2 - Finding area Determine the area of the shaded...Ch. 6.2 - Finding area Determine the area of the shaded...Ch. 6.2 - Finding area Determine the area of the shaded...Ch. 6.2 - Prob. 30ECh. 6.2 - Prob. 31ECh. 6.2 - Prob. 32ECh. 6.2 - Area between velocity curves Two runners, starting...Ch. 6.2 - Prob. 34ECh. 6.2 - Prob. 35ECh. 6.2 - Calculus and geometry For the given regions R1 and...Ch. 6.2 - Regions between curves Find the area of the region...Ch. 6.2 - Prob. 38ECh. 6.2 - Regions between curves Find the area of the region...Ch. 6.2 - Regions between curves Find the area of the region...Ch. 6.2 - Regions between curves Find the area of the region...Ch. 6.2 - Regions between curves Find the area of the region...Ch. 6.2 - Regions between curves Find the area of the region...Ch. 6.2 - Prob. 44ECh. 6.2 - Regions between curves Find the area of the region...Ch. 6.2 - Regions between curves Find the area of the region...Ch. 6.2 - Prob. 47ECh. 6.2 - Prob. 48ECh. 6.2 - Any method Use any method (including geometry) to...Ch. 6.2 - Prob. 50ECh. 6.2 - Prob. 51ECh. 6.2 - Prob. 52ECh. 6.2 - Regions between curves Find the area of the region...Ch. 6.2 - Regions between curves Find the area of the region...Ch. 6.2 - Regions between curves Find the area of the region...Ch. 6.2 - Prob. 56ECh. 6.2 - Regions between curves Find the area of the region...Ch. 6.2 - Prob. 58ECh. 6.2 - Prob. 59ECh. 6.2 - Prob. 60ECh. 6.2 - Regions between curves Find the area of the region...Ch. 6.2 - Prob. 62ECh. 6.2 - Prob. 63ECh. 6.2 - Prob. 64ECh. 6.2 - Prob. 65ECh. 6.2 - Prob. 66ECh. 6.2 - Prob. 67ECh. 6.2 - Prob. 68ECh. 6.2 - Prob. 69ECh. 6.2 - Prob. 70ECh. 6.2 - Prob. 71ECh. 6.2 - Prob. 72ECh. 6.2 - Prob. 73ECh. 6.2 - Prob. 74ECh. 6.2 - Prob. 75ECh. 6.2 - Prob. 76ECh. 6.2 - Prob. 77ECh. 6.2 - Prob. 78ECh. 6.3 - Why is the volume as given by the general slicing...Ch. 6.3 - In Example 2 what is the cross-sectional area...Ch. 6.3 - What solid results when the region R is revolved...Ch. 6.3 - Prob. 4QCCh. 6.3 - Prob. 5QCCh. 6.3 - Prob. 6QCCh. 6.3 - Suppose a cut is made through a solid object...Ch. 6.3 - A solid has a circular base and cross sections...Ch. 6.3 - Consider a solid whose base is the region in the...Ch. 6.3 - Why is the disk method a special case of the...Ch. 6.3 - Prob. 5ECh. 6.3 - Prob. 6ECh. 6.3 - Use the region R that is bounded by the graphs of...Ch. 6.3 - Use the region R that is bounded by the graphs of...Ch. 6.3 - Use the region R that is bounded by the graphs of...Ch. 6.3 - Prob. 10ECh. 6.3 - General slicing method Use the general slicing...Ch. 6.3 - General slicing method Use the general slicing...Ch. 6.3 - General slicing method Use the general slicing...Ch. 6.3 - General slicing method Use the general slicing...Ch. 6.3 - General slicing method Use the general slicing...Ch. 6.3 - Prob. 16ECh. 6.3 - Disk method Let R be the region bounded by the...Ch. 6.3 - Disk method Let R be the region bounded by the...Ch. 6.3 - Disk method Let R be the region bounded by the...Ch. 6.3 - Solids of revolution Let R be the region bounded...Ch. 6.3 - Solids of revolution Let R be the region bounded...Ch. 6.3 - Disks/washers about the y-axis Let R be the region...Ch. 6.3 - Washer method Let R be the region bounded by the...Ch. 6.3 - Washer method Let R be the region bounded by the...Ch. 6.3 - Washer method Let R be the region bounded by the...Ch. 6.3 - Washer method Let R be the region bounded by the...Ch. 6.3 - Solids of revolution Let R be the region bounded...Ch. 6.3 - Disks/washers about the y-axis Let R be the region...Ch. 6.3 - Disk method Let R be the region bounded by the...Ch. 6.3 - Prob. 30ECh. 6.3 - Disk method Let R be the region bounded by the...Ch. 6.3 - Solids of revolution Let R be the region bounded...Ch. 6.3 - Solids of revolution Let R be the region bounded...Ch. 6.3 - Washer method Let R be the region bounded by the...Ch. 6.3 - Washer method Let R be the region bounded by the...Ch. 6.3 - Washer method Let R be the region bounded by the...Ch. 6.3 - Disks/washers about the y-axis Let R be the region...Ch. 6.3 - Solids of revolution Let R be the region bounded...Ch. 6.3 - Solids of revolution Let R be the region bounded...Ch. 6.3 - Solids of revolution Let R be the region bounded...Ch. 6.3 - Solids of revolution Let R be the region bounded...Ch. 6.3 - Solids of revolution Let R be the region bounded...Ch. 6.3 - Solids of revolution Let R be the region bounded...Ch. 6.3 - Solids of revolution Let R be the region bounded...Ch. 6.3 - Which is greater? For the following regions R,...Ch. 6.3 - Which is greater? For the following regions R,...Ch. 6.3 - Prob. 47ECh. 6.3 - Prob. 48ECh. 6.3 - Revolution about other axes Let R be the region...Ch. 6.3 - Prob. 50ECh. 6.3 - Revolution about other axes Let R be the region...Ch. 6.3 - Prob. 52ECh. 6.3 - Prob. 53ECh. 6.3 - Prob. 54ECh. 6.3 - Revolution about other axes Find the volume of the...Ch. 6.3 - Revolution about other axes Find the volume of the...Ch. 6.3 - Prob. 57ECh. 6.3 - Prob. 58ECh. 6.3 - Prob. 59ECh. 6.3 - Prob. 60ECh. 6.3 - Prob. 61ECh. 6.3 - Prob. 62ECh. 6.3 - Prob. 63ECh. 6.3 - Prob. 64ECh. 6.3 - Prob. 65ECh. 6.3 - Prob. 66ECh. 6.3 - Prob. 67ECh. 6.3 - Volume of a wooden object A solid wooden object...Ch. 6.3 - Prob. 69ECh. 6.3 - Water in a bowl A hemispherical bowl of radius 8...Ch. 6.3 - Prob. 71ECh. 6.3 - Prob. 72ECh. 6.3 - Cavalieris principle Cavalieris principle states...Ch. 6.3 - Prob. 74ECh. 6.4 - The triangle bounded by the x-axis, the line y =...Ch. 6.4 - Prob. 2QCCh. 6.4 - Prob. 3QCCh. 6.4 - Assume f and g are continuous with f(x) g(x) on...Ch. 6.4 - Fill in the blanks: A region R is revolved about...Ch. 6.4 - Fill in the blanks: A region R is revolved about...Ch. 6.4 - Look again at the region R in Figure 6.38 (p 439)....Ch. 6.4 - Let R be the region in the first quadrant bounded...Ch. 6.4 - Let R be the region bounded by the curves...Ch. 6.4 - Prob. 7ECh. 6.4 - Let R be the region bounded by the curves...Ch. 6.4 - Shell method Let R be the region bounded by the...Ch. 6.4 - Prob. 10ECh. 6.4 - Shell method Let R be the region bounded by the...Ch. 6.4 - Prob. 12ECh. 6.4 - Shell method Let R be the region bounded by the...Ch. 6.4 - Prob. 14ECh. 6.4 - Shell method Let R be the region bounded by the...Ch. 6.4 - Prob. 16ECh. 6.4 - Shell method Let R be the region bounded by the...Ch. 6.4 - Prob. 18ECh. 6.4 - Shell method Let R be the region bounded by the...Ch. 6.4 - Prob. 20ECh. 6.4 - Shell method Let R be the region bounded by the...Ch. 6.4 - Shell method Let R be the region bounded by the...Ch. 6.4 - Shell method Let R be the region bounded by the...Ch. 6.4 - Shell method Let R be the region bounded by the...Ch. 6.4 - Prob. 25ECh. 6.4 - Prob. 26ECh. 6.4 - Shell method Let R be the region bounded by the...Ch. 6.4 - Prob. 28ECh. 6.4 - Prob. 29ECh. 6.4 - Prob. 30ECh. 6.4 - Prob. 31ECh. 6.4 - Prob. 32ECh. 6.4 - Prob. 33ECh. 6.4 - Prob. 34ECh. 6.4 - Washers vs. shells Let R be the region bounded by...Ch. 6.4 - Prob. 36ECh. 6.4 - Washers vs. shells Let R be the region bounded by...Ch. 6.4 - Prob. 38ECh. 6.4 - Shell method about other lines Let R be the region...Ch. 6.4 - Prob. 40ECh. 6.4 - Prob. 41ECh. 6.4 - Prob. 42ECh. 6.4 - Prob. 43ECh. 6.4 - Prob. 44ECh. 6.4 - Prob. 45ECh. 6.4 - Prob. 46ECh. 6.4 - Prob. 47ECh. 6.4 - Prob. 48ECh. 6.4 - Volume of a sphere Let R be the region bounded by...Ch. 6.4 - Prob. 50ECh. 6.4 - A torus (doughnut) A torus is formed when a circle...Ch. 6.4 - Prob. 52ECh. 6.4 - Prob. 53ECh. 6.4 - Prob. 54ECh. 6.4 - Choose your method Find the volume of the...Ch. 6.4 - Prob. 56ECh. 6.4 - Prob. 57ECh. 6.4 - Prob. 58ECh. 6.4 - Choose your method Let R be the region bounded by...Ch. 6.4 - Prob. 60ECh. 6.4 - Choose your method Let R be the region bounded by...Ch. 6.4 - Prob. 62ECh. 6.4 - Prob. 63ECh. 6.4 - Prob. 64ECh. 6.4 - Prob. 65ECh. 6.4 - Prob. 66ECh. 6.4 - Prob. 67ECh. 6.4 - Prob. 68ECh. 6.4 - Prob. 69ECh. 6.4 - Prob. 70ECh. 6.4 - Prob. 71ECh. 6.4 - Equal integrals Without evaluating integrals,...Ch. 6.4 - Volumes without calculus Solve the following...Ch. 6.4 - Prob. 74ECh. 6.4 - Prob. 75ECh. 6.4 - Prob. 76ECh. 6.5 - What does the arc length formula give for the...Ch. 6.5 - Prob. 2QCCh. 6.5 - Prob. 3QCCh. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - Setting up arc length integrals Write and...Ch. 6.5 - Setting up arc length integrals Write and...Ch. 6.5 - Setting up arc length integrals Write and...Ch. 6.5 - Prob. 6ECh. 6.5 - Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Arc lezngth calculations Find the arc length of...Ch. 6.5 - Arc length calculations Find the arc length of the...Ch. 6.5 - Arc length calculations Find the arc length of the...Ch. 6.5 - Arc length calculations Find the arc length of the...Ch. 6.5 - Arc length calculations Find the arc length of the...Ch. 6.5 - Arc length calculations Find the arc length of the...Ch. 6.5 - Arc length calculations Find the arc length of the...Ch. 6.5 - Arc length calculations Find the arc length of the...Ch. 6.5 - Arc length calculations with respect to y Find the...Ch. 6.5 - Arc length calculations with respect to y Find the...Ch. 6.5 - Arc length calculations with respect to y Find the...Ch. 6.5 - Arc length calculations with respect to y Find the...Ch. 6.5 - Arc length by calculator a. Write and simplify the...Ch. 6.5 - Prob. 22ECh. 6.5 - Prob. 23ECh. 6.5 - Prob. 24ECh. 6.5 - Arc length by calculator a. Write and simplify the...Ch. 6.5 - Arc length by calculator a. Write and simplify the...Ch. 6.5 - Arc length by calculator a. Write and simplify the...Ch. 6.5 - Prob. 28ECh. 6.5 - Arc length by calculator a. Write and simplify the...Ch. 6.5 - Arc length by calculator a.Write and simplify the...Ch. 6.5 - Prob. 31ECh. 6.5 - Prob. 32ECh. 6.5 - Explain why or why not Determine whether the...Ch. 6.5 - Prob. 34ECh. 6.5 - Functions from arc length What differentiable...Ch. 6.5 - Function from arc length Find a curve that passes...Ch. 6.5 - Prob. 37ECh. 6.5 - Prob. 38ECh. 6.5 - Prob. 39ECh. 6.5 - Prob. 40ECh. 6.5 - Prob. 41ECh. 6.5 - Bernoullis parabolas Johann Bernoulli (16671748)...Ch. 6.6 - Which is greater the surface area of a cone of...Ch. 6.6 - Prob. 2QCCh. 6.6 - Prob. 3QCCh. 6.6 - Prob. 1ECh. 6.6 - Prob. 2ECh. 6.6 - Prob. 3ECh. 6.6 - Prob. 4ECh. 6.6 - Prob. 5ECh. 6.6 - Prob. 6ECh. 6.6 - Prob. 7ECh. 6.6 - Prob. 8ECh. 6.6 - Computing surface areas Find the area of the...Ch. 6.6 - Computing surface areas Find the area of the...Ch. 6.6 - Revolving about the y-axis Find the area of the...Ch. 6.6 - Prob. 12ECh. 6.6 - Computing surface areas Find the area of the...Ch. 6.6 - Prob. 14ECh. 6.6 - Prob. 15ECh. 6.6 - Prob. 16ECh. 6.6 - Prob. 17ECh. 6.6 - Prob. 18ECh. 6.6 - Prob. 19ECh. 6.6 - Prob. 20ECh. 6.6 - Painting surfaces A 1.5-mm layer of paint is...Ch. 6.6 - Prob. 22ECh. 6.6 - Explain why or why not Determine whether the...Ch. 6.6 - T 2629. Surface area using technology Consider the...Ch. 6.6 - T 2629. Surface area using technology Consider the...Ch. 6.6 - Surface area using technology Consider the...Ch. 6.6 - Surface area using technology Consider the...Ch. 6.6 - Surface area using technology Consider the...Ch. 6.6 - Revolving an astroid Consider the upper half of...Ch. 6.6 - Prob. 30ECh. 6.6 - Prob. 31ECh. 6.6 - Prob. 32ECh. 6.6 - Prob. 33ECh. 6.6 - Prob. 34ECh. 6.6 - Prob. 35ECh. 6.6 - Prob. 36ECh. 6.6 - Prob. 37ECh. 6.6 - Prob. 38ECh. 6.6 - Surface-area-to-volume ratio (SAV) In the design...Ch. 6.6 - Prob. 40ECh. 6.6 - Prob. 41ECh. 6.6 - Surface plus cylinder Suppose f is a nonnegative...Ch. 6.7 - In Figure 6.69, suppose a = 0, b = 3, and the...Ch. 6.7 - Prob. 2QCCh. 6.7 - Prob. 3QCCh. 6.7 - Prob. 4QCCh. 6.7 - In Example 3b, the bucket occupies the interval...Ch. 6.7 - Prob. 6QCCh. 6.7 - Prob. 7QCCh. 6.7 - Suppose a 1-m cylindrical bar has a constant...Ch. 6.7 - Explain how to find the mass of a one-dimensional...Ch. 6.7 - How much work is required to move an object from x...Ch. 6.7 - Why is integration used to find the work done by a...Ch. 6.7 - Why is integration used to find the work required...Ch. 6.7 - Prob. 6ECh. 6.7 - What is the pressure on a horizontal surface with...Ch. 6.7 - Prob. 8ECh. 6.7 - Consider the cylindrical tank in Example 4 that...Ch. 6.7 - Consider the cylindrical tank in Example 4 that...Ch. 6.7 - Consider the cylindrical tank in Example 4 that...Ch. 6.7 - Prob. 12ECh. 6.7 - Mass of one-dimensional objects Find the mass of...Ch. 6.7 - Mass of one-dimensional objects Find the mass of...Ch. 6.7 - Mass of one-dimensional objects Find the mass of...Ch. 6.7 - Prob. 16ECh. 6.7 - Mass of one-dimensional objects Find the mass of...Ch. 6.7 - Mass of one-dimensional objects Find the mass of...Ch. 6.7 - Mass of one-dimensional objects Find the mass of...Ch. 6.7 - Prob. 20ECh. 6.7 - Work from force How much work is required to move...Ch. 6.7 - Prob. 22ECh. 6.7 - Compressing and stretching a spring Suppose a...Ch. 6.7 - Compressing and stretching a spring Suppose a...Ch. 6.7 - Prob. 25ECh. 6.7 - Prob. 26ECh. 6.7 - Prob. 27ECh. 6.7 - Prob. 28ECh. 6.7 - Calculating work for different springs Calculate...Ch. 6.7 - Prob. 30ECh. 6.7 - Winding a chain A 30-m-long chain hangs vertically...Ch. 6.7 - Prob. 32ECh. 6.7 - Winding part of a chain A 20-m-long, 50-kg chain...Ch. 6.7 - Leaky Bucket A 1-kg bucket resting on the ground...Ch. 6.7 - Emptying a swimming pool A swimming pool has the...Ch. 6.7 - Prob. 36ECh. 6.7 - Emptying a half-full cylindrical tank Suppose the...Ch. 6.7 - Prob. 38ECh. 6.7 - Emptying a conical tank A water tank is shaped...Ch. 6.7 - Prob. 40ECh. 6.7 - Filling a spherical tank A spherical water tank...Ch. 6.7 - Emptying a water trough A water trough has a...Ch. 6.7 - Emptying a water trough A cattle trough has a...Ch. 6.7 - Prob. 44ECh. 6.7 - Emptying a conical tank An inverted cone is 2 m...Ch. 6.7 - Force on dams The following figures show the shape...Ch. 6.7 - Force on dams The following figures show the shape...Ch. 6.7 - Force on dams The following figures show the shape...Ch. 6.7 - Force on dams The following figures show the shape...Ch. 6.7 - Prob. 50ECh. 6.7 - Prob. 51ECh. 6.7 - Prob. 52ECh. 6.7 - Prob. 53ECh. 6.7 - Prob. 54ECh. 6.7 - Prob. 55ECh. 6.7 - Prob. 56ECh. 6.7 - Prob. 57ECh. 6.7 - Prob. 58ECh. 6.7 - Prob. 59ECh. 6.7 - Prob. 60ECh. 6.7 - Prob. 61ECh. 6.7 - Prob. 62ECh. 6.7 - Drinking juice A glass has circular cross sections...Ch. 6.7 - Prob. 64ECh. 6.7 - Prob. 65ECh. 6.7 - Prob. 66ECh. 6.7 - Prob. 67ECh. 6.7 - Work by two different integrals A rigid body with...Ch. 6.7 - Work in a gravitational field For large distances...Ch. 6.7 - Prob. 70ECh. 6 - Explain why or why not Determine whether the...Ch. 6 - Prob. 2RECh. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Prob. 5RECh. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - Prob. 9RECh. 6 - Prob. 10RECh. 6 - Prob. 11RECh. 6 - Prob. 12RECh. 6 - Prob. 13RECh. 6 - Prob. 14RECh. 6 - Prob. 15RECh. 6 - Prob. 16RECh. 6 - Prob. 17RECh. 6 - Prob. 18RECh. 6 - Prob. 19RECh. 6 - Prob. 20RECh. 6 - Prob. 21RECh. 6 - Prob. 22RECh. 6 - Prob. 23RECh. 6 - Prob. 24RECh. 6 - Prob. 25RECh. 6 - Prob. 26RECh. 6 - Prob. 27RECh. 6 - Multiple regions The regions R1, R2, and R3 (see...Ch. 6 - Prob. 29RECh. 6 - Prob. 30RECh. 6 - Prob. 31RECh. 6 - Prob. 32RECh. 6 - Prob. 33RECh. 6 - Prob. 34RECh. 6 - Prob. 35RECh. 6 - Area and volume Let R be the region in the first...Ch. 6 - Prob. 37RECh. 6 - Prob. 38RECh. 6 - Prob. 39RECh. 6 - Prob. 40RECh. 6 - Prob. 41RECh. 6 - Prob. 42RECh. 6 - Prob. 43RECh. 6 - Prob. 44RECh. 6 - Prob. 45RECh. 6 - Prob. 46RECh. 6 - Prob. 47RECh. 6 - Prob. 48RECh. 6 - Prob. 49RECh. 6 - Prob. 50RECh. 6 - Prob. 51RECh. 6 - Prob. 52RECh. 6 - Prob. 53RECh. 6 - Prob. 54RECh. 6 - Prob. 55RECh. 6 - Prob. 56RECh. 6 - Prob. 57RECh. 6 - Prob. 58RECh. 6 - Prob. 59RECh. 6 - Prob. 60RECh. 6 - Prob. 61RECh. 6 - Prob. 62RECh. 6 - Prob. 63RECh. 6 - Prob. 64RECh. 6 - Prob. 65RECh. 6 - Surface area and volume Let f(x)=13x3 and let R be...Ch. 6 - Surface area and volume Let f(x)=3xx2 and let R be...Ch. 6 - Prob. 68RECh. 6 - Surface area and more Let f(x)=x42+116x2 and let R...Ch. 6 - Prob. 70RECh. 6 - Prob. 71RECh. 6 - Prob. 72RECh. 6 - Prob. 73RECh. 6 - Leaky bucket A 1-kg bucket resting on the ground...Ch. 6 - Prob. 75RECh. 6 - Prob. 76RECh. 6 - Pumping water A water tank has the shape of a box...Ch. 6 - Prob. 78RECh. 6 - Prob. 79RECh. 6 - Prob. 80RECh. 6 - Prob. 81RECh. 6 - Prob. 82RECh. 6 - Fluid Forces Suppose the Mowing plates are placed...Ch. 6 - Prob. 84RECh. 6 - Prob. 85RECh. 6 - Prob. 86RE
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- (10) (16 points) Let R>0. Consider the truncated sphere S given as x² + y² + (z = √15R)² = R², z ≥0. where F(x, y, z) = −yi + xj . (a) (8 points) Consider the vector field V (x, y, z) = (▼ × F)(x, y, z) Think of S as a hot-air balloon where the vector field V is the velocity vector field measuring the hot gasses escaping through the porous surface S. The flux of V across S gives the volume flow rate of the gasses through S. Calculate this flux. Hint: Parametrize the boundary OS. Then use Stokes' Theorem. (b) (8 points) Calculate the surface area of the balloon. To calculate the surface area, do the following: Translate the balloon surface S by the vector (-15)k. The translated surface, call it S+ is part of the sphere x² + y²+z² = R². Why do S and S+ have the same area? ⚫ Calculate the area of S+. What is the natural spherical parametrization of S+?arrow_forward(1) (8 points) Let c(t) = (et, et sint, et cost). Reparametrize c as a unit speed curve starting from the point (1,0,1).arrow_forward(9) (16 points) Let F(x, y, z) = (x² + y − 4)i + 3xyj + (2x2 +z²)k = - = (x²+y4,3xy, 2x2 + 2²). (a) (4 points) Calculate the divergence and curl of F. (b) (6 points) Find the flux of V x F across the surface S given by x² + y²+2² = 16, z ≥ 0. (c) (6 points) Find the flux of F across the boundary of the unit cube E = [0,1] × [0,1] x [0,1].arrow_forward
- (8) (12 points) (a) (8 points) Let C be the circle x² + y² = 4. Let F(x, y) = (2y + e²)i + (x + sin(y²))j. Evaluate the line integral JF. F.ds. Hint: First calculate V x F. (b) (4 points) Let S be the surface r² + y² + z² = 4, z ≤0. Calculate the flux integral √(V × F) F).dS. Justify your answer.arrow_forwardDetermine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle. a = 13, b = 15, C = 68° Law of Sines Law of Cosines Then solve the triangle. (Round your answers to four decimal places.) C = 15.7449 A = 49.9288 B = 62.0712 × Need Help? Read It Watch Itarrow_forward(4) (10 points) Evaluate √(x² + y² + z²)¹⁄² exp[}(x² + y² + z²)²] dV where D is the region defined by 1< x² + y²+ z² ≤4 and √√3(x² + y²) ≤ z. Note: exp(x² + y²+ 2²)²] means el (x²+ y²+=²)²]¸arrow_forward
- (2) (12 points) Let f(x,y) = x²e¯. (a) (4 points) Calculate Vf. (b) (4 points) Given x directional derivative 0, find the line of vectors u = D₁f(x, y) = 0. (u1, 2) such that the - (c) (4 points) Let u= (1+3√3). Show that Duƒ(1, 0) = ¦|▼ƒ(1,0)| . What is the angle between Vf(1,0) and the vector u? Explain.arrow_forwardFind the missing values by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.) a b 29 39 66.50 C 17.40 d 0 54.0 126° a Ꮎ b darrow_forward(5) (10 points) Let D be the parallelogram in the xy-plane with vertices (0, 0), (1, 1), (1, 1), (0, -2). Let f(x,y) = xy/2. Use the linear change of variables T(u, v)=(u,u2v) = (x, y) 1 to calculate the integral f(x,y) dA= 0 ↓ The domain of T is a rectangle R. What is R? |ǝ(x, y) du dv. |ð(u, v)|arrow_forward
- 2 Anot ined sove in peaper PV+96252 Q3// Find the volume of the region between the cylinder z = y2 and the xy- plane that is bounded by the planes x=1, x=2,y=-2,andy=2. vertical rect a Q4// Draw and Evaluate Soxy-2sin (ny2)dydx D Lake tarrow_forwardDetermine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle. B 13 cm 97° Law of Sines Law of Cosines A 43° Then solve the triangle. (Round your answers to two decimal places.) b = x C = A = 40.00arrow_forwardFind the missing values by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.) a 29 b 39 d Ꮎ 126° a Ꮎ b darrow_forward
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