Single Variable Calculus
8th Edition
ISBN: 9781305266636
Author: James Stewart
Publisher: Cengage Learning
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Chapter 8.3, Problem 10E
A vertical plate is submerged (or partially submerged) in water and has the indicated shape. Explain how to approximate the hydrostatic force against one side of the plate by a Riemann sum. Then express the force as an
10. 
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x³-343
If k(x) =
x-7
complete the table and use the results to find lim k(x).
X-7
x
6.9
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7.001
7.01
7.1
k(x)
Complete the table.
X
6.9
6.99
6.999
7.001
7.01
7.1
k(x)
(Round to three decimal places as needed.)
(3) (4 points) Given three vectors a, b, and c, suppose:
|bx c = 2
|a|=√√8
• The angle between a and b xc is 0 = 135º.
.
Calculate the volume a (bxc) of the parallelepiped spanned by the three vectors.
Calculate these limits. If the limit is ∞ or -∞, write infinity or-infinity. If the limit does not exist, write DNE:
Hint: Remember the first thing you check when you are looking at a limit of a quotient is the limit value of the denominator.
1. If the denominator does not go to 0, you should be able to right down the answer immediately.
2. If the denominator goes to 0, but the numerator does not, you will have to check the sign (±) of the quotient, from both sides if the limit is not one-sided.
3. If both the numerator and the denominator go to 0, you have to do the algebraic trick of rationalizing.
So, group your limits into these three forms and work with them one group at a time.
(a) lim
t-pi/2
sint-√ sin 2t+14cos ² t
7
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(b) lim
sint + sin 2t+14cos
=
∞
t-pi/2
2
2cos t
(c) lim
cost-√sin 2t+14cos² t
=
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2cos t
(d) lim
t→pi/2
cost+√ sin t + 14cos
2cos ² t
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sint-v sin
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0
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(f) lim
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Chapter 8 Solutions
Single Variable Calculus
Ch. 8.1 - Use the arc length formula (3) to find the length...Ch. 8.1 - Use the arc length formula to find the length of...Ch. 8.1 - Set up an integral that represents the length of...Ch. 8.1 - Set up an integral that represents the length of...Ch. 8.1 - Set up an integral that represents the length of...Ch. 8.1 - Set up an integral that represents the length of...Ch. 8.1 - Set up an integral that represents the length of...Ch. 8.1 - Set up an integral that represents the length of...Ch. 8.1 - Find the exact length of the curve. 9. y = 1 +...Ch. 8.1 - Find the exact length of the curve. 10. 36y2 = (x2...
Ch. 8.1 - Find the exact length of the curve. 11....Ch. 8.1 - Find the exact length of the curve. 12....Ch. 8.1 - Find the exact length of the curve. 13....Ch. 8.1 - Find the exact length of the curve. 14. y = ln(cos...Ch. 8.1 - Find the exact length of the curve. 15. y = ln(sec...Ch. 8.1 - Find the exact length of the curve. 16....Ch. 8.1 - Find the exact length of the curve. 17....Ch. 8.1 - Find the exact length of the curve. 18....Ch. 8.1 - Find the exact length of the curve. 19....Ch. 8.1 - Find the exact length of the curve. 20. y = 1 ex,...Ch. 8.1 - Find the length of the arc of the curve from point...Ch. 8.1 - Find the length of the arc of the curve from point...Ch. 8.1 - Graph the curve and visually estimate its length....Ch. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - Prob. 27ECh. 8.1 - Prob. 28ECh. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - Prob. 33ECh. 8.1 - (a) Sketch the curve y3 = x2. (b) Use Formulas 3...Ch. 8.1 - Find the arc length function for the curve y =...Ch. 8.1 - (a) Find the arc length function for the curve y =...Ch. 8.1 - Find the arc length function for the curve...Ch. 8.1 - The arc length function for a curve y = f(x),...Ch. 8.1 - Prob. 39ECh. 8.1 - A steady wind blows a kite due west. The kites...Ch. 8.1 - A hawk flying at 15 m/s at an altitude of 180 m...Ch. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - (a) The figure shows a telephone wire hanging...Ch. 8.1 - Prob. 45ECh. 8.1 - The curves with equations x + y = l , n = 4, 6, 8,...Ch. 8.2 - (a) Set up an integral for the area of the surface...Ch. 8.2 - (a) Set up an integral for the area of the surface...Ch. 8.2 - (a) Set up an integral for the area of the surface...Ch. 8.2 - (a) Set up an integral for the area of the surface...Ch. 8.2 - (a) Set up an integral for the area of the surface...Ch. 8.2 - (a) Set up an integral for the area of the surface...Ch. 8.2 - Prob. 7ECh. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Prob. 9ECh. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Prob. 11ECh. 8.2 - Find the exact area of the surface obtained by...Ch. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.2 - The given curve is rotated about the y-axis. Find...Ch. 8.2 - The given curve is rotated about the y-axis. Find...Ch. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - Prob. 21ECh. 8.2 - Prob. 22ECh. 8.2 - Prob. 23ECh. 8.2 - Prob. 24ECh. 8.2 - If the region R=(x,y)x1,0y1/x is rotated about the...Ch. 8.2 - If the infinite curve y = ex, x 0, is rotated...Ch. 8.2 - Prob. 29ECh. 8.2 - A group of engineers is building a parabolic...Ch. 8.2 - (a) The ellipsex2a2+y2b2=1abis rotated about the...Ch. 8.2 - Prob. 32ECh. 8.2 - If the curve y = f(x), a x b, is rotated about...Ch. 8.2 - Prob. 35ECh. 8.2 - Prob. 36ECh. 8.2 - Prob. 37ECh. 8.2 - Prob. 38ECh. 8.2 - Formula 4 is valid only when f(x) 0. Show that...Ch. 8.3 - An aquarium 5 ft long, 2 ft wide, and 3 ft deep is...Ch. 8.3 - A tank is 8 m long, 4 m wide, 2 m high, and...Ch. 8.3 - A vertical plate is submerged (or partially...Ch. 8.3 - A vertical plate is submerged (or partially...Ch. 8.3 - A vertical plate is submerged (or partially...Ch. 8.3 - A vertical plate is submerged (or partially...Ch. 8.3 - A vertical plate is submerged (or partially...Ch. 8.3 - A vertical plate is submerged (or partially...Ch. 8.3 - A vertical plate is submerged (or partially...Ch. 8.3 - A vertical plate is submerged (or partially...Ch. 8.3 - A vertical plate is submerged (or partially...Ch. 8.3 - A milk truck carries milk with density 64.6 lb/ft3...Ch. 8.3 - A trough is filled with a liquid of density 840...Ch. 8.3 - A vertical dam has a semicircular gate as shown in...Ch. 8.3 - Prob. 15ECh. 8.3 - Prob. 16ECh. 8.3 - A swimming pool is 20 ft wide and 40 ft long and...Ch. 8.3 - Prob. 18ECh. 8.3 - A metal plate was found submerged vertically in...Ch. 8.3 - Prob. 20ECh. 8.3 - Point-masses mi are located on the x-axis as...Ch. 8.3 - Point-masses mi are located on the x-axis as...Ch. 8.3 - The masses mi are located at the points Pi. Find...Ch. 8.3 - Prob. 24ECh. 8.3 - Sketch the region bounded by the curves, and...Ch. 8.3 - Prob. 26ECh. 8.3 - Prob. 27ECh. 8.3 - Sketch the region bounded by the curves, and...Ch. 8.3 - Prob. 29ECh. 8.3 - Prob. 30ECh. 8.3 - Find the centroid of the region bounded by the...Ch. 8.3 - Prob. 32ECh. 8.3 - Prob. 33ECh. 8.3 - Calculate the moments Mx and My and the center of...Ch. 8.3 - Calculate the moments Mx and My and the center of...Ch. 8.3 - Use Simpsons Rule to estimate the centroid of the...Ch. 8.3 - Find the centroid of the region bounded by the...Ch. 8.3 - Prob. 38ECh. 8.3 - Prove that the centroid of any triangle is located...Ch. 8.3 - Find the centroid of the region shown, not by...Ch. 8.3 - Find the centroid of the region shown, not by...Ch. 8.3 - Prob. 42ECh. 8.3 - Prob. 43ECh. 8.3 - Prob. 44ECh. 8.3 - Prob. 45ECh. 8.3 - Prob. 46ECh. 8.3 - Prob. 47ECh. 8.3 - The Second Theorem of Pappus is in the same spirit...Ch. 8.3 - Prob. 49ECh. 8.3 - Prob. 50ECh. 8.3 - Prob. 51ECh. 8.4 - The marginal cost function C(x) was defined to be...Ch. 8.4 - Prob. 2ECh. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - Prob. 6ECh. 8.4 - If a supply curve is modeled by the equation p =...Ch. 8.4 - In a purely competitive market, the price of a...Ch. 8.4 - Prob. 9ECh. 8.4 - A camera company estimates that the demand...Ch. 8.4 - Prob. 11ECh. 8.4 - A movie theater has been charging 10.00 per person...Ch. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - Prob. 15ECh. 8.4 - Prob. 16ECh. 8.4 - Prob. 17ECh. 8.4 - A hot, wet summer is causing a mosquito population...Ch. 8.4 - Prob. 19ECh. 8.4 - Prob. 20ECh. 8.4 - The dye dilution method is used to measure cardiac...Ch. 8.4 - Prob. 22ECh. 8.4 - The graph of the concentration function c(t) is...Ch. 8.5 - Let f (x) be the probability density function for...Ch. 8.5 - Let f(t) be the probability density function for...Ch. 8.5 - Prob. 3ECh. 8.5 - The density function f(x)=e3x(1+e3x)2 is an...Ch. 8.5 - Let f (x) = c/(1 + x2). (a) For what value of c is...Ch. 8.5 - Let f(x) = k (3x x2) if 0 x 3 and f(x) = 0 if x...Ch. 8.5 - Prob. 7ECh. 8.5 - (a) Explain why the function whose graph is shown...Ch. 8.5 - Show that the median waiting time for a phone call...Ch. 8.5 - (a) A type of light bulb is labeled as having an...Ch. 8.5 - Prob. 11ECh. 8.5 - The time between infection and the display of...Ch. 8.5 - REM sleep is the phase of sleep when most active...Ch. 8.5 - According to the National Health Survey, the...Ch. 8.5 - The Garbage Project at the University of Arizona...Ch. 8.5 - Boxes are labeled as containing 500 g of cereal....Ch. 8.5 - Prob. 17ECh. 8.5 - Prob. 18ECh. 8.5 - Prob. 19ECh. 8.5 - Prob. 20ECh. 8.5 - Prob. 21ECh. 8 - (a) How is the length of a curve defined? (b)...Ch. 8 - Prob. 2RCCCh. 8 - Prob. 3RCCCh. 8 - (a) What is the physical significance of the...Ch. 8 - Prob. 5RCCCh. 8 - Prob. 6RCCCh. 8 - Prob. 7RCCCh. 8 - Prob. 8RCCCh. 8 - Prob. 9RCCCh. 8 - Prob. 10RCCCh. 8 - Prob. 1RECh. 8 - Prob. 2RECh. 8 - Prob. 3RECh. 8 - Prob. 4RECh. 8 - Prob. 5RECh. 8 - Prob. 6RECh. 8 - Prob. 7RECh. 8 - Prob. 8RECh. 8 - Prob. 9RECh. 8 - Prob. 10RECh. 8 - A gate in an irrigation canal is constructed in...Ch. 8 - A trough is filled with water and its vertical...Ch. 8 - Find the centroid of the region shown. 13.Ch. 8 - Prob. 14RECh. 8 - Prob. 15RECh. 8 - Prob. 16RECh. 8 - Prob. 17RECh. 8 - Prob. 18RECh. 8 - Prob. 19RECh. 8 - After a 6-mg injection of dye into a heart, the...Ch. 8 - (a) Explain why the function...Ch. 8 - Lengths of human pregnancies are normally...Ch. 8 - The length of time spent waiting in line at a...Ch. 8 - Prob. 1PCh. 8 - Prob. 2PCh. 8 - If a sphere of radius r is sliced by a plane whose...Ch. 8 - (a) Show that an observer at height H above the...Ch. 8 - Prob. 5PCh. 8 - The figure shows a semicircle with radius 1,...Ch. 8 - Prob. 7PCh. 8 - Consider a flat metal plate to be placed...Ch. 8 - A uniform disk with radius 1 m is to be cut by a...Ch. 8 - Prob. 10PCh. 8 - In a famous 18th-century problem, known as Buffons...Ch. 8 - Prob. 12PCh. 8 - Prob. 13P
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