Cálculo Vol 2 12 Ed - George Thomas - SOLUTIONS - Ebook download as PDF File .pdf), Download as PDF, TXT or read online from Scribd . a" œ 1, a# œ 1, a$ œ 1 b 1 œ 2, a% œ 2 b 1 œ 3, a& œ 3 b 2 œ 5, a' œ 8, a(œ 13, a) œ Cálculo Vol. 2 - George B. Thomas - 11ª Edição by danielle_silva_ Copyright: © All Rights Reserved. Download as PDF or read online from Scribd. Flag for. Download Cálculo - Volume 2 - 11ª Edição - George B. Thomas.
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Solucionário de Cálculo - Volume 1 - 11ª edição - George Thomas PART TWO Thomas' Calculus, Eleventh Edition, and Thomas' Calculus: Early T ranscendentals, Eleventh ARDIS • BORZELLINO • BUCHANAN • MOGILL • N ELSON. Exercícios Resolvidos - Livro Cálculo - George B. Thomas - Vol 1 - 11th - parte 4 2 2 2 2 2 1 \u2c6 \uc da b\ufffd in¸ 3 (d) V C y dy 4 2 4 2 4 50x x# # #1 1 1 1# #' \ufffd25 25 A-PDF Split DEMO: download from www. Exercícios Resolvidos - Livro Cálculo - George B. Thomas - Vol 1 - 11th - parte 5 muscpertastsunear.tk 10/15/04 AM Page 2 A-PDF Split.
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Exercícios Resolvidos - Livro Cálculo - George B. Thomas - Vol 1 - 11th - parte 5
Theworkandmaterialsfromitshouldneverbemadeavailableto students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials. The corresponding Student's Solutions Manual omits the solutions to the even-numbered exercises as well as the solutions to the CAS exercises because the CAS command templates would give them all away.
In addition to including the solutions to all of the new exercises in this edition of Thomas, we have carefully revised or Every CAS exercise is solved in both the MAPLE and computer algebra systems. Step 3: Step 4: Step 5: Step 6: TaylorApproximation f x.
Recall that c must be a value between 0 and x. The following analyzes the derivatives to determine their maximum values. A three dimensional look at the error functions. See Exercise Using the Ratio Test: Here is a Maple CAS procedure to produce these approximations: The series for e sin x converges for all values of x.
The given series does not converge absolutely by the Direct Comparison Test since the nth term of a divergent series. Therefore the convergence is conditional. The series does not converge absolutely: Consider b x 3! The given series has the form x c b x 2! The given series has the form 1 b x b xn n " 1bx " The given series has the form x c x 3! The given series has the form 1 c x 2! Yes, the series! No, the series! Split the given series into! Therefore, 3. A polynomial has only a finite number of nonzero terms in its Taylor series, but the functions sin x, ln x and ex have infinitely many nonzero terms in their Taylor expansions.
Chapter 11 Parametric Equations and Polar Coordinates b 9. One possible parameterization is: Substituting t for y. For simplicity. Substituting t for x. Drop a vertical line from the point ax. Extend the vertical line through A to the x-axis and let C be the point of intersection. Substitution yields y s In terms of. Since we only want the top half of a circle. The equation of the line through a0. So that we can start at a1. Since we only need to go from a1.
Since we want x to stay between c3 and 3. Draw line AM in the figure and note that nAMO is a right angle since it is an inscribed angle which spans the diameter of a circle. In triangle BPO. Let denote the angle through which the wheel turns. Let the x-axis be the line the wheel rolls along with the y-axis through a low point of the trochoid see the accompanying figure.
Next introduce xw yw -axes parallel to the xy-axes and having their origin at the center C of the wheel. The curve's mass dt dt.
Chapter 11 Parametric Equations and Polar Coordinates tt: For example. Instead the interval generates the half-line from B to c b c 1. Chapter 11 Parametric Equatins and Polar Coordinates Chapter 11 Parametric Equations and Polar Coordinates y x The area of the inscribed rectangle is given by since the length is 2x and the height is 2y.
Since the plate is symmetric about the y-axis. Moment of the strip about the x-axis: Foci a! Vertices a! Chapter 11 Practice Exercises Chapter 11 Parametric Equations and Polar Coordinates 5.
The circle lies interior to the cardioid. Chapter 11 Parametric Equations and Polar Coordinates 8 Chapter 11 Practice Exercises x b y Draw the horizontal line through P and let it intersect the y-axis in point C.
Vertices are a!
Cálculo 2 - George B. Thomas - 11a Edição.pdf -
Chapter 11 Additional and Advanced Exercises b Around the y-axis: Chapter 11 Additional and Advanced Exercises The x-axis 4. In fact it should lie on the line segment between a0. All vectors must be drawn to scale. The vector v is horizontal and 1 in. The vectors u and w are the horizontal. They are all 1 in. Draw to scale. Solving the first equation for lF2 l results in: Substituting this Solving the first equation for lF1 l results in: Substituting this result into the second equation gives us: Since u was assumed to be any unit vector in the plane.
Let V". Let u be any unit vector in the plane.
If u is positioned so that its initial point is at the origin and terminal point is at ax. The sum of two vectors of equal length is always orthogonal to their difference. CA and CB are orthogonal. Chapter 12 Vectors and the Geometry of Space 1 2 u 9. What is not as obvious is the statement that equal diagonals happen only in a rectangle.
In the case of nonzero vectors. Suppose the diagonals of a rectangle are perpendicular. Clearly the diagonals of a rectangle are equal in length. We show this is true by letting the adjacent sides of a parallelogram be the vectors v" i b v j and u" i b u j.
In either case. The cross product is not associative. The direction 2j b k and P! The applicable sign ensures the area formula gives a nonnegative number.
Select a point on either line. The planes are perpendicular when their normals are perpendicular. L1 and L2 are skew. One is found as follows: If v" and v are nonzero vectors parallel to the lines. Since the plane passes through the origin. Since a.
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Since it meets the plane M at a right angle. There are many possible answers. We calculate the volume by the disk method: For fixed z. We calculate the volume by the slicing method. To insert the stated function. This built-in function requires the loading of a special graphics package. In the following chapter. For the purposes of plotting the functions of two variables expressed implicitly in this section.
Chapter 12 Practice Exercises 2. Chapter 12 Practice Exercises Information from ship A indicates the submarine is now on the line L": At mph. Substituting this result into the 5 5 4 9 second equation gives us: Solving the first equation for lT2 l results in: After 6 hours.
Let L": Chapter 12 Additional and Advanced Exercises the second equation gives us: Let the coordinates of D be given by aa. Add the two equations 2 Substituting this value for b in the first equation gives us: B and C. The formula is always true.
If a graph is too small. The unit vectors i. Cos[t] b t Sin[t]. For 39 and Leave a space between a and t and b and t. Sin[a t]. The same percentage will approximately v! Then we want the factor p so that pv! R cos!
When marble A is located R units downrange. R v cos! To find the flight time we find the time when the projectile lands: The range is largest when sin 2! Therefore v! If x is [cos 2! Eliminating the parameter!. These equations describe parametrically the points on a curve in the xy-plane associated with the maximum heights on the parabolic trajectories in v 16g! It will take the ball 4. According to part d.
Then the range is about xa1. At those times the ball is about xa0. At that time the ball will be The range is about xa3. The range is 1 about xa3. If R is any antiderivative of r. To find the wind needed for a home run. If U t is an antiderivative of r t on I. Let P t! Cut the cylinder along PQ and flatten.
For graphing. By Exercise 9 in Section By Exercise 12 in Section By Exercise 10 in Section By Exercise 11 in Section By Exercise 16 in Section By Exercise 15 in Section By Exercise 13 in Section If the car is moving along a curved path. By Exercise 14 in Section Since the curve is a plane curve.
From Exercise From Example 1.
If a plane curve is sufficiently differentiable the torsion is zero as the following argument shows: Let be the angle between r and a. For To get the z-level curves here. Write the function f[x.. If f is continuous at x! The equation of any line through a0. If f is not continuous at! If the first partial derivatives are continuous throughout an open region R.
Chapter 14 Partial Derivatives To find! Using the result in Exercise Du fa1. The directional derivative is the scalar component. We cannot use the second derivative test. For interior points of the rectangular region. Therefore the absolute maximum is 11 at!
For interior critical points we have: See Exercise 45 above: Dxx ac3. Dxy a3. Only a0. Dxy ac3.
Dyy ac3.Both series have nonnegative terms for 3. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs.
Books by George B. Thomas Jr.
To get the z-level curves here. Therefore no maximum or minimum value exists subject to the constraint. Jump to Page. Theworkandmaterialsfromitshouldneverbemadeavailableto students except by instructors using the accompanying text in their classes. Let the x-axis be the line the wheel rolls along with the y-axis through a low point of the trochoid see the accompanying figure.
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