Thomas' Calculus (14th Edition)
14th Edition
ISBN: 9780134438986
Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher: PEARSON
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Chapter 11, Problem 13AAE
To determine
To draw: The graph of given equation
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The cup on the 9th hole of a golf course is located dead center in the middle of a circular green which is 40 feet in radius. Your ball is located as in the picture below. The ball follows a straight line path and exits the green at the right-most edge. Assume the ball travels 8 ft/sec.
Introduce coordinates so that the cup is the origin of an xy-coordinate system and start by writing down the equations of the circle and the linear path of the ball. Provide numerical answers below with two decimal places of accuracy.
50 feet
green
ball
40 feet
9
cup
ball path
rough
(a) The x-coordinate of the position where the ball enters the green will be
(b) The ball will exit the green exactly
seconds after it is hit.
(c) Suppose that L is a line tangent to the boundary of the golf green and parallel to the path of the ball. Let Q be the point where the line is tangent to the circle. Notice that there are two possible positions for Q. Find the possible x-coordinates of Q:
smallest x-coordinate =…
Draw the unit circle and plot the point P=(8,2). Observe there are TWO lines tangent to the circle passing through the point P. Answer the questions below with 3 decimal places of accuracy.
P
L1
L
(a) The line L₁ is tangent to the unit circle at the point
(b) The tangent line L₁ has equation:
X +
(c) The line L₂ is tangent to the unit circle at the point (
(d) The tangent line 42 has equation:
y=
x +
).
What is a solution to a differential equation? We said that a differential equation is an equation that
describes the derivative, or derivatives, of a function that is unknown to us. By a solution to a differential
equation, we mean simply a function that satisfies this description.
2. Here is a differential equation which describes an unknown position function s(t):
ds
dt
318
4t+1,
ds
(a) To check that s(t) = 2t2 + t is a solution to this differential equation, calculate
you really do get 4t +1.
and check that
dt'
(b) Is s(t) = 2t2 +++ 4 also a solution to this differential equation?
(c) Is s(t)=2t2 + 3t also a solution to this differential equation?
ds
1
dt
(d) To find all possible solutions, start with the differential equation = 4t + 1, then move dt to the
right side of the equation by multiplying, and then integrate both sides. What do you get?
(e) Does this differential equation have a unique solution, or an infinite family of solutions?
Chapter 11 Solutions
Thomas' Calculus (14th Edition)
Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Prob. 3ECh. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Prob. 6ECh. 11.1 - Prob. 7ECh. 11.1 - Prob. 8ECh. 11.1 - Prob. 9ECh. 11.1 - Finding Cartesian from Parametric...
Ch. 11.1 - Prob. 11ECh. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Prob. 13ECh. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Prob. 15ECh. 11.1 - Prob. 16ECh. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - In Exercises 19–24, match the parametric equations...Ch. 11.1 - In Exercises 19–24, match the parametric equations...Ch. 11.1 - In Exercises 19–24, match the parametric equations...Ch. 11.1 - In Exercises 19–24, match the parametric equations...Ch. 11.1 - In Exercises 19–24, match the parametric equations...Ch. 11.1 - In Exercises 19–24, match the parametric equations...Ch. 11.1 - In Exercises 25–28, use the given graphs of x =...Ch. 11.1 - In Exercises 25–28, use the given graphs of x =...Ch. 11.1 - In Exercises 25–28, use the given graphs of x =...Ch. 11.1 - In Exercises 25–28, use the given graphs of x =...Ch. 11.1 - Finding Parametric Equations
Find parametric...Ch. 11.1 - Find parametric equations and a parameter interval...Ch. 11.1 - In Exercises 31–36, find a parametrization for the...Ch. 11.1 - In Exercises 31–36, find a parametrization for the...Ch. 11.1 - In Exercises 31–36, find a parametrization for the...Ch. 11.1 - In Exercises 31–36, find a parametrization for the...Ch. 11.1 - In Exercises 31-36, find a parametrization for the...Ch. 11.1 - In Exercises 31-36, find a parametrization for the...Ch. 11.1 - Find parametric equations and a parameter interval...Ch. 11.1 - Find parametric equations and a parameter interval...Ch. 11.1 - Find parametric equations for the...Ch. 11.1 - Find parametric equations tor the circle
using as...Ch. 11.1 - Find a parametrization for the line segment...Ch. 11.1 - Find a parametrization for the curve with...Ch. 11.1 - Find a parametrization for the circle (x − 2)2 +...Ch. 11.1 - Find a parametrization for the circle x2 + y2 = 1...Ch. 11.1 - The witch of Maria Agnesi The bell-shaped witch of...Ch. 11.1 - Hypocycloid When a circle rolls on the inside of a...Ch. 11.1 - Prob. 47ECh. 11.1 - Trochoids A wheel of radius a rolls along a...Ch. 11.1 - Find the point on the parabola x = t, y = t2, −∞ <...Ch. 11.1 - Find the point on the ellipse x = 2 cos t, y = sin...Ch. 11.1 - Prob. 51ECh. 11.1 - Prob. 52ECh. 11.1 - Prob. 53ECh. 11.1 - If you have a parametric equation grapher, graph...Ch. 11.1 - Deltoid
x = 2 cos t + cos 2t, y = 2 sin t − sin...Ch. 11.1 - Prob. 56ECh. 11.1 - a. Epicycloid
x = 9 cos t − cos 9t, y = 9 sin t −...Ch. 11.1 - a. x = 6 cos t + 5 cos 3t, y = 6 sin t − 5 sin...Ch. 11.2 - In Exercises 1–14, find an equation for the line...Ch. 11.2 - In Exercises 1–14, find an equation for the line...Ch. 11.2 - In Exercises 1–14, find an equation for the line...Ch. 11.2 - In Exercises 1–14, find an equation for the line...Ch. 11.2 - In Exercises 1–14, find an equation for the line...Ch. 11.2 - In Exercises 1–14, find an equation for the line...Ch. 11.2 - In Exercises 1–14, find an equation for the line...Ch. 11.2 - In Exercises 1–14, find an equation for the line...Ch. 11.2 - In Exercises 1–14, find an equation for the line...Ch. 11.2 - In Exercises 1–14, find an equation for the line...Ch. 11.2 - Prob. 11ECh. 11.2 - In Exercises 1–14, find an equation for the line...Ch. 11.2 - Prob. 13ECh. 11.2 - In Exercises 1–14, find an equation for the line...Ch. 11.2 - Assuming that the equations in Exercises 15–20...Ch. 11.2 - Assuming that the equations in Exercises 15–20...Ch. 11.2 - Assuming that the equations in Exercises 15–20...Ch. 11.2 - Assuming that the equations in Exercises 15–20...Ch. 11.2 - Assuming that the equations in Exercises 15–20...Ch. 11.2 - Assuming that the equations in Exercises 15–20...Ch. 11.2 - Find the area under one arch of the cycloid
Ch. 11.2 - Find the area enclosed by the y-axis and the...Ch. 11.2 - Find the area enclosed by the ellipse
Ch. 11.2 - Find the area under y = x3 over [0, 1] using the...Ch. 11.2 - Find the lengths of the curves in Exercises...Ch. 11.2 - Find the lengths of the curves in Exercises...Ch. 11.2 - Find the lengths of the curves in Exercises...Ch. 11.2 - Find the lengths of the curves in Exercises...Ch. 11.2 - Find the lengths of the curves in Exercises...Ch. 11.2 - Find the lengths of the curves in Exercises...Ch. 11.2 - Find the areas of the surfaces generated by...Ch. 11.2 - Prob. 32ECh. 11.2 - Find the areas of the surfaces generated by...Ch. 11.2 - Prob. 34ECh. 11.2 - Prob. 35ECh. 11.2 - Prob. 36ECh. 11.2 - Prob. 37ECh. 11.2 - Prob. 38ECh. 11.2 - Prob. 39ECh. 11.2 - Prob. 40ECh. 11.2 - Length is independent of parametrization To...Ch. 11.2 - Prob. 42ECh. 11.2 - The curve with parametric equations
is called a...Ch. 11.2 - Prob. 44ECh. 11.2 - Prob. 45ECh. 11.2 - Prob. 46ECh. 11.2 - Prob. 47ECh. 11.2 - Prob. 48ECh. 11.2 - Prob. 49ECh. 11.2 - Prob. 50ECh. 11.3 - Prob. 1ECh. 11.3 - Prob. 2ECh. 11.3 - Prob. 3ECh. 11.3 - Prob. 4ECh. 11.3 - Prob. 5ECh. 11.3 - Prob. 6ECh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Find the polar coordinates, and , of the...Ch. 11.3 - Prob. 11ECh. 11.3 - Prob. 12ECh. 11.3 - Prob. 13ECh. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Prob. 16ECh. 11.3 - Prob. 17ECh. 11.3 - Prob. 18ECh. 11.3 - Prob. 19ECh. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Replace the polar equations in Exercises 27–52...Ch. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Replace the polar equations in Exercises 27–52...Ch. 11.3 - Prob. 32ECh. 11.3 - Prob. 33ECh. 11.3 - Replace the polar equations in Exercises 27–52...Ch. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - Replace the polar equations in Exercises 27–52...Ch. 11.3 - Prob. 38ECh. 11.3 - Replace the polar equations in Exercises 27–52...Ch. 11.3 - Prob. 40ECh. 11.3 - Prob. 41ECh. 11.3 - Prob. 42ECh. 11.3 - Replace the polar equations in Exercises 27–52...Ch. 11.3 - Replace the polar equations in Exercises 27–52...Ch. 11.3 - Prob. 45ECh. 11.3 - Prob. 46ECh. 11.3 - Replace the polar equations in Exercises 27–52...Ch. 11.3 - Replace the polar equations in Exercises 27–52...Ch. 11.3 - Replace the polar equations in Exercises 27–52...Ch. 11.3 - Prob. 50ECh. 11.3 - Prob. 51ECh. 11.3 - Prob. 52ECh. 11.3 - Replace the Cartesian equations in Exercises 53–66...Ch. 11.3 - Prob. 54ECh. 11.3 - Prob. 55ECh. 11.3 - Prob. 56ECh. 11.3 - Prob. 57ECh. 11.3 - Prob. 58ECh. 11.3 - Prob. 59ECh. 11.3 - Prob. 60ECh. 11.3 - Prob. 61ECh. 11.3 - Prob. 62ECh. 11.3 - Prob. 63ECh. 11.3 - Prob. 64ECh. 11.3 - Prob. 65ECh. 11.3 - Prob. 66ECh. 11.3 - Prob. 67ECh. 11.3 - Prob. 68ECh. 11.4 - Prob. 1ECh. 11.4 - Prob. 2ECh. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Find the slopes of the curves in Exercises 17-20...Ch. 11.4 - Find the slopes of the curves in Exercises 17-20...Ch. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Prob. 21ECh. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - Prob. 27ECh. 11.4 - Prob. 28ECh. 11.4 - Prob. 29ECh. 11.4 - Prob. 30ECh. 11.4 - Prob. 31ECh. 11.4 - Prob. 32ECh. 11.4 - Which of the following has the same graph as r = 1...Ch. 11.4 - Prob. 34ECh. 11.4 - Prob. 35ECh. 11.4 - Prob. 36ECh. 11.4 - Roses Graph the roses r = cos mθ for m = 1/3, 2,...Ch. 11.4 - Spirals Polar coordinates are just the thing for...Ch. 11.4 - Graph the equation for 0 ≤ θ 14 π.
Ch. 11.4 - Prob. 40ECh. 11.5 - Finding Polar Areas
Find the areas of the regions...Ch. 11.5 - Finding Polar Areas
Find the areas of the regions...Ch. 11.5 - Prob. 3ECh. 11.5 - Prob. 4ECh. 11.5 - Prob. 5ECh. 11.5 - Prob. 6ECh. 11.5 - Prob. 7ECh. 11.5 - Prob. 8ECh. 11.5 - Find the areas of the regions in Exercises...Ch. 11.5 - Find the areas of the regions in Exercises...Ch. 11.5 - Find the areas of the regions in Exercises...Ch. 11.5 - Find the areas of the regions in Exercises...Ch. 11.5 - Find the areas of the regions in Exercises...Ch. 11.5 - Find the areas of the regions in Exercises...Ch. 11.5 - Find the areas of the regions in Exercises...Ch. 11.5 - Find the areas of the regions in Exercises...Ch. 11.5 - Find the areas of the regions in Exercises...Ch. 11.5 - Find the areas of the regions in Exercises...Ch. 11.5 - Prob. 19ECh. 11.5 - Find the areas of the regions in Exercises...Ch. 11.5 - Find the lengths of the curves in Exercises...Ch. 11.5 - Find the lengths of the curves in Exercises...Ch. 11.5 - Prob. 23ECh. 11.5 - Find the lengths of the curves in Exercises...Ch. 11.5 - Prob. 25ECh. 11.5 - Prob. 26ECh. 11.5 - Find the lengths of the curves in Exercises...Ch. 11.5 - Find the lengths of the curves in Exercises...Ch. 11.5 - Prob. 29ECh. 11.5 - Prob. 30ECh. 11.5 - Prob. 31ECh. 11.5 - Prob. 32ECh. 11.6 - Match the parabolas in Exercises 1–4 with the...Ch. 11.6 - Match the parabolas in Exercises 1–4 with the...Ch. 11.6 - Match the parabolas in Exercises 1–4 with the...Ch. 11.6 - Match the parabolas in Exercises 1–4 with the...Ch. 11.6 - Match each conic section in Exercises 5–8 with one...Ch. 11.6 - Match each conic section in Exercises 5–8 with one...Ch. 11.6 - Match each conic section in Exercises 5–8 with one...Ch. 11.6 - Match each conic section in Exercises 5–8 with one...Ch. 11.6 - Exercises 9–16 give equations of parabolas. Find...Ch. 11.6 - Prob. 10ECh. 11.6 - Exercises 9–16 give equations of parabolas. Find...Ch. 11.6 - Prob. 12ECh. 11.6 - Exercises 9–16 give equations of parabolas. Find...Ch. 11.6 - Prob. 14ECh. 11.6 - Exercises 9–16 give equations of parabolas. Find...Ch. 11.6 - Prob. 16ECh. 11.6 - Prob. 17ECh. 11.6 - Prob. 18ECh. 11.6 - Exercises 17–24 give equations for ellipses. Put...Ch. 11.6 - Prob. 20ECh. 11.6 - Exercises 17–24 give equations for ellipses. Put...Ch. 11.6 - Prob. 22ECh. 11.6 - Exercises 17–24 give equations for ellipses. Put...Ch. 11.6 - Prob. 24ECh. 11.6 - Exercises 25 and 26 give information about the...Ch. 11.6 - Prob. 26ECh. 11.6 - Prob. 27ECh. 11.6 - Prob. 28ECh. 11.6 - Prob. 29ECh. 11.6 - Prob. 30ECh. 11.6 - Prob. 31ECh. 11.6 - Prob. 32ECh. 11.6 - Prob. 33ECh. 11.6 - Prob. 34ECh. 11.6 - Prob. 35ECh. 11.6 - Prob. 36ECh. 11.6 - Exercises 35–38 give information about the foci,...Ch. 11.6 - Exercises 35–38 give information about the foci,...Ch. 11.6 - The parabola y2 = 8x is shifted down 2 units and...Ch. 11.6 - Prob. 40ECh. 11.6 - Prob. 41ECh. 11.6 - Prob. 42ECh. 11.6 - Prob. 43ECh. 11.6 - Prob. 44ECh. 11.6 - Prob. 45ECh. 11.6 - Exercises 39–42 give equations for parabolas and...Ch. 11.6 - Prob. 47ECh. 11.6 - Prob. 48ECh. 11.6 - Prob. 49ECh. 11.6 - Prob. 50ECh. 11.6 - Prob. 51ECh. 11.6 - Prob. 52ECh. 11.6 - Prob. 53ECh. 11.6 - Prob. 54ECh. 11.6 - Prob. 55ECh. 11.6 - Prob. 56ECh. 11.6 - Prob. 57ECh. 11.6 - Prob. 58ECh. 11.6 - Prob. 59ECh. 11.6 - Prob. 60ECh. 11.6 - Prob. 61ECh. 11.6 - Prob. 62ECh. 11.6 - Prob. 63ECh. 11.6 - Prob. 64ECh. 11.6 - Prob. 65ECh. 11.6 - Prob. 66ECh. 11.6 - Prob. 67ECh. 11.6 - Prob. 68ECh. 11.6 - Prob. 69ECh. 11.6 - Prob. 70ECh. 11.6 - Prob. 71ECh. 11.6 - Prob. 72ECh. 11.6 - Prob. 73ECh. 11.6 - Prob. 74ECh. 11.6 - Prob. 75ECh. 11.6 - Prob. 76ECh. 11.6 - Prob. 77ECh. 11.6 - Prob. 78ECh. 11.6 - Prob. 79ECh. 11.6 - Prob. 80ECh. 11.6 - Prob. 81ECh. 11.7 - Prob. 1ECh. 11.7 - Prob. 2ECh. 11.7 - Prob. 3ECh. 11.7 - Prob. 4ECh. 11.7 - Prob. 5ECh. 11.7 - Prob. 6ECh. 11.7 - Prob. 7ECh. 11.7 - Prob. 8ECh. 11.7 - Exercises 9–12 give the foci or vertices and the...Ch. 11.7 - Prob. 10ECh. 11.7 - Prob. 11ECh. 11.7 - Prob. 12ECh. 11.7 - Prob. 13ECh. 11.7 - Prob. 14ECh. 11.7 - Prob. 15ECh. 11.7 - Prob. 16ECh. 11.7 - Prob. 17ECh. 11.7 - Prob. 18ECh. 11.7 - Prob. 19ECh. 11.7 - Prob. 20ECh. 11.7 - Prob. 21ECh. 11.7 - Prob. 22ECh. 11.7 - Prob. 23ECh. 11.7 - Prob. 24ECh. 11.7 - Prob. 25ECh. 11.7 - Prob. 26ECh. 11.7 - Prob. 27ECh. 11.7 - Prob. 28ECh. 11.7 - Prob. 29ECh. 11.7 - Prob. 30ECh. 11.7 - Prob. 31ECh. 11.7 - Prob. 32ECh. 11.7 - Prob. 33ECh. 11.7 - Prob. 34ECh. 11.7 - Prob. 35ECh. 11.7 - Prob. 36ECh. 11.7 - Prob. 37ECh. 11.7 - Sketch the parabolas and ellipses in Exercises...Ch. 11.7 - Prob. 39ECh. 11.7 - Prob. 40ECh. 11.7 - Sketch the parabolas and ellipses in Exercises...Ch. 11.7 - Prob. 42ECh. 11.7 - Prob. 43ECh. 11.7 - Prob. 44ECh. 11.7 - Prob. 45ECh. 11.7 - Prob. 46ECh. 11.7 - Prob. 47ECh. 11.7 - Prob. 48ECh. 11.7 - Prob. 49ECh. 11.7 - Prob. 50ECh. 11.7 - Prob. 51ECh. 11.7 - Prob. 52ECh. 11.7 - Prob. 53ECh. 11.7 - Prob. 54ECh. 11.7 - Prob. 55ECh. 11.7 - Prob. 56ECh. 11.7 - Prob. 57ECh. 11.7 - Prob. 58ECh. 11.7 - Prob. 59ECh. 11.7 - Prob. 60ECh. 11.7 - Prob. 61ECh. 11.7 - Prob. 62ECh. 11.7 - Prob. 63ECh. 11.7 - Prob. 64ECh. 11.7 - Prob. 65ECh. 11.7 - Prob. 66ECh. 11.7 - Prob. 67ECh. 11.7 - Prob. 68ECh. 11.7 - Prob. 69ECh. 11.7 - Prob. 70ECh. 11.7 - Prob. 71ECh. 11.7 - Prob. 72ECh. 11.7 - Prob. 73ECh. 11.7 - Prob. 74ECh. 11.7 - Prob. 75ECh. 11.7 - Prob. 76ECh. 11 - Prob. 1GYRCh. 11 - Give some typical parametrizations for lines,...Ch. 11 - Prob. 3GYRCh. 11 - What is the formula for the slope dy/dx of a...Ch. 11 - Prob. 5GYRCh. 11 - Prob. 6GYRCh. 11 - Prob. 7GYRCh. 11 - Prob. 8GYRCh. 11 - Prob. 9GYRCh. 11 - Prob. 10GYRCh. 11 - Prob. 11GYRCh. 11 - Prob. 12GYRCh. 11 - Prob. 13GYRCh. 11 - Prob. 14GYRCh. 11 - Prob. 15GYRCh. 11 - Prob. 16GYRCh. 11 - Prob. 17GYRCh. 11 - Prob. 18GYRCh. 11 - Prob. 19GYRCh. 11 - Prob. 1PECh. 11 - Prob. 2PECh. 11 - Prob. 3PECh. 11 - Prob. 4PECh. 11 - Prob. 5PECh. 11 - Prob. 6PECh. 11 - Prob. 7PECh. 11 - Prob. 8PECh. 11 - Prob. 9PECh. 11 - Prob. 10PECh. 11 - Prob. 11PECh. 11 - Prob. 12PECh. 11 - Prob. 13PECh. 11 - Prob. 14PECh. 11 - Prob. 15PECh. 11 - Prob. 16PECh. 11 - Prob. 17PECh. 11 - Prob. 18PECh. 11 - Prob. 19PECh. 11 - Prob. 20PECh. 11 - Prob. 21PECh. 11 - Prob. 22PECh. 11 - Prob. 23PECh. 11 - Prob. 24PECh. 11 - Prob. 25PECh. 11 - Prob. 26PECh. 11 - Prob. 27PECh. 11 - Prob. 28PECh. 11 - Prob. 29PECh. 11 - Prob. 30PECh. 11 - Prob. 31PECh. 11 - Prob. 32PECh. 11 - Prob. 33PECh. 11 - Prob. 34PECh. 11 - Prob. 35PECh. 11 - Prob. 36PECh. 11 - Prob. 37PECh. 11 - Prob. 38PECh. 11 - Match each graph in Exercises 39–46 with the...Ch. 11 - Prob. 40PECh. 11 - Prob. 41PECh. 11 - Prob. 42PECh. 11 - Prob. 43PECh. 11 - Prob. 44PECh. 11 - Prob. 45PECh. 11 - Prob. 46PECh. 11 - Prob. 47PECh. 11 - Prob. 48PECh. 11 - Prob. 49PECh. 11 - Prob. 50PECh. 11 - Prob. 51PECh. 11 - Prob. 52PECh. 11 - Prob. 53PECh. 11 - Prob. 54PECh. 11 - Prob. 55PECh. 11 - Prob. 56PECh. 11 - Prob. 57PECh. 11 - Prob. 58PECh. 11 - Prob. 59PECh. 11 - Prob. 60PECh. 11 - Prob. 61PECh. 11 - Prob. 62PECh. 11 - Prob. 63PECh. 11 - Prob. 64PECh. 11 - Prob. 65PECh. 11 - Prob. 66PECh. 11 - Prob. 67PECh. 11 - Prob. 68PECh. 11 - Prob. 69PECh. 11 - Prob. 70PECh. 11 - Prob. 71PECh. 11 - Prob. 72PECh. 11 - Prob. 73PECh. 11 - Prob. 74PECh. 11 - Prob. 75PECh. 11 - Prob. 76PECh. 11 - Prob. 77PECh. 11 - Prob. 78PECh. 11 - Prob. 79PECh. 11 - Prob. 80PECh. 11 - Prob. 81PECh. 11 - Prob. 82PECh. 11 - Prob. 83PECh. 11 - Prob. 84PECh. 11 - Prob. 85PECh. 11 - Prob. 86PECh. 11 - Prob. 87PECh. 11 - Prob. 88PECh. 11 - Prob. 1AAECh. 11 - Prob. 2AAECh. 11 - Prob. 3AAECh. 11 - Prob. 4AAECh. 11 - Prob. 5AAECh. 11 - Prob. 6AAECh. 11 - Prob. 7AAECh. 11 - Prob. 8AAECh. 11 - Prob. 9AAECh. 11 - Prob. 10AAECh. 11 - Prob. 11AAECh. 11 - Prob. 12AAECh. 11 - Prob. 13AAECh. 11 - Prob. 14AAECh. 11 - Prob. 15AAECh. 11 - Prob. 16AAECh. 11 - Prob. 17AAECh. 11 - Prob. 18AAECh. 11 - Prob. 19AAECh. 11 - Prob. 20AAECh. 11 - Prob. 21AAECh. 11 - Prob. 22AAECh. 11 - Epicycloids When a circle rolls externally along...Ch. 11 - Prob. 24AAECh. 11 - Prob. 25AAECh. 11 - Prob. 26AAECh. 11 - Prob. 27AAECh. 11 - Prob. 28AAECh. 11 - Prob. 29AAECh. 11 - Prob. 30AAE
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Calculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. Freeman
Calculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning
What is Ellipse?; Author: Don't Memorise;https://www.youtube.com/watch?v=nzwCInIMlU4;License: Standard YouTube License, CC-BY