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Calculus

Here are the best study resources to pass Calculus. Find Calculus study guides, notes, assignments, and much more.

 Calculus > QUESTIONS & ANSWERS > Chapter 4: APPLICATIONS OF DIFFERENTIATION. WOrk and Answers (All)
Chapter 4: APPLICATIONS OF DIFFERENTIATION. WOrk and Answers

4.1 Maximum and Minimum Values 1. A function  has an absolute minimum at  =  if () is the smallest function value on the entire domain of , whereas  has a local minimum at  if () is the sm...

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 Calculus > QUESTIONS & ANSWERS > Chapter 5 INTEGRALS. Work and Answers (All)
Chapter 5 INTEGRALS. Work and Answers

5.1 Areas and Distances 1. (a) Since  is decreasing , we can obtain a lower estimate by using right endpoints. We are instructed to use five rectangles, so  = 5. 5 = 5 =1 ()∆ ∆ =  −...

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 Calculus > QUESTIONS & ANSWERS > Chapter 6: APPLICATIONS OF INTEGRATION. Work and Answers (All)
Chapter 6: APPLICATIONS OF INTEGRATION. Work and Answers

6.1 Areas Between Curves 1.  = =1 =8( − ) = 18 √3  − 1  = 3 443 − ln||8 1 = (12 − ln 8) − 3 4 − ln 1 = 45 4 − ln 8 2.  = 01  − 2  =  − 1 221 0 =  − 1 2 −...

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 Calculus > QUESTIONS & ANSWERS > Chapter 7: TECHNIQUES OF INTEGRATION. Work and Answers (All)
Chapter 7: TECHNIQUES OF INTEGRATION. Work and Answers

7.1 Integration by Parts 1. Let  = ,  = 2  ⇒  = ,  = 1 22. Then by Equation 2,  2  = 1 22 −  1 22  = 1 22 − 1 42 + . 2. Let  = ln,  = √  ⇒  = 1  , ...

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 Calculus > QUESTIONS & ANSWERS > Chapter 8 FURTHER APPLICATIONS OF INTEGRATION. Work and Answers (All)
Chapter 8 FURTHER APPLICATIONS OF INTEGRATION. Work and Answers

8.1 Arc Length 1.  = 2 − 5 ⇒  = −31 1 + ()2  = −31 1 + (2)2  = √5 [3 − (−1)] = 4√5. The arc length can be calculated using the distance formula, since the curve is a line segment, so...

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 Calculus > QUESTIONS & ANSWERS > Chapter 9: DIFFERENTIAL EQUATIONS. Work and Answers (All)
Chapter 9: DIFFERENTIAL EQUATIONS. Work and Answers

9.1 Modeling with Differential Equations 1.  = 2 3  + −2 ⇒ 0 = 2 3  − 2−2. To show that  is a solution of the differential equation, we will substitute the expressions for  and 0 in the...

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 Calculus > QUESTIONS & ANSWERS > Chapter 10: PARAMETRIC EQUATIONS AND POLAR COORDINATES. Work and Answers (All)
Chapter 10: PARAMETRIC EQUATIONS AND POLAR COORDINATES. Work and Answers

10.1 Curves Defined by Parametric Equations 1.  = 1 − 2,  = 2 − 2, −1 ≤  ≤ 2  −1 0 1 2  0 1 0 −3  −3 0 1 0 2.  = 3 + ,  = 2 + 2, −2 ≤  ≤ 2  −2 −1 0 1 2  −10 −2 0 2 10  6 3 2...

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 Calculus > QUESTIONS & ANSWERS > Chapter 11: INFINITE SEQUENCES AND SERIES. Work and Answers (All)
Chapter 11: INFINITE SEQUENCES AND SERIES. Work and Answers

11.1 Sequences 1. (a) A sequence is an ordered list of numbers. It can also be defined as a function whose domain is the set of positive integers. (b) The terms  approach 8 as  becomes large. In...

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 Calculus > QUESTIONS & ANSWERS > Chapter 12: VECTORS AND THE GEOMETRY OF SPACE. Work and Answers (All)
Chapter 12: VECTORS AND THE GEOMETRY OF SPACE. Work and Answers

12.1 Three-Dimensional Coordinate Systems 1. We start at the origin, which has coordinates (0 0 0). First we move 4 units along the positive -axis, affecting only the -coordinate, bringing us t...

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 Calculus > QUESTIONS & ANSWERS > Chapter 13: VECTOR FUNCTIONS. Work and Answers (All)
Chapter 13: VECTOR FUNCTIONS. Work and Answers

13.1 Vector Functions and Space Curves 1. The component functions ln( + 1), √9− 2 , and 2 are all defined when  + 1  0 ⇒   −1 and 9 − 2  0 ⇒ −3    3, so the domain of r is (−13). 2. T...

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 Calculus > QUESTIONS & ANSWERS > Capter 14: PARTIAL DERIVATIVES. Work and Answers (All)
Capter 14: PARTIAL DERIVATIVES. Work and Answers

14.1 Functions of Several Variables 1. (a) From Table 1, (−1540) = −27, which means that if the temperature is −15◦C and the wind speed is 40 kmh, then the air would feel equivalent to approximat...

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 Calculus > QUESTIONS & ANSWERS > Chapter 15: MULTIPLE INTEGRALS. Work and Answers (All)
Chapter 15: MULTIPLE INTEGRALS. Work and Answers

15.1 Double Integrals over Rectangles 1. (a) The subrectangles are shown in the figure. The surface is the graph of ( ) =  and ∆ = 4, so we estimate  ≈ 3  = 1 2  = 1 ( )∆ =...

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 Calculus > QUESTIONS & ANSWERS > Chapter 16: VECTOR CALCULUS. Work and Answers (All)
Chapter 16: VECTOR CALCULUS. Work and Answers

16.1 Vector Fields 1. F( ) = 03i − 04j All vectors in this field are identical, with length 05 and parallel to h3 −4i. 2. F( ) = 1 2i +  j The length of the vector 1 2i +  j is  1...

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 Calculus > QUESTIONS & ANSWERS > Chapter 17: SECOND-ORDER DIFFERENTIAL EQUATIONS. Work and Answers (All)
Chapter 17: SECOND-ORDER DIFFERENTIAL EQUATIONS. Work and Answers

17.1 Second-Order Linear Equations 1. The auxiliary equation is 2 −  − 6 = 0 ⇒ ( − 3)( + 2) = 0 ⇒  = 3,  = −2. Then by (8) the general solution is  = 13 + 2−2. 2. The auxiliary equatio...

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 Calculus > QUESTIONS & ANSWERS > Stewart - Calculus 8e ET Chapter 1. All Answers (All)
Stewart - Calculus 8e ET Chapter 1. All Answers

Stewart - Calculus 8e ET Chapter 1 Form A © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 1....

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 Calculus > QUESTIONS & ANSWERS > Stewart - Calculus 8e ET Chapter 2. All Answers (All)
Stewart - Calculus 8e ET Chapter 2. All Answers

1. Find the limit. 2. Evaluate the limit. 3. Find the limit. 4. How close to do we have to take x so that 5. How close to 2 do we have to take x so that is within a distance of 0.01 from 13? 6. I...

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 Calculus > QUESTIONS & ANSWERS > Stewart - Calculus 8e ET Chapter 3. All Answers (All)
Stewart - Calculus 8e ET Chapter 3. All Answers

1. Find the first and the second derivatives of the function. 2. Find an equation of the tangent line to the curve. 3. Find 4. Find all points at which the tangent line is horizontal on the graph o...

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 Calculus > QUESTIONS & ANSWERS > Stewart - Calculus 8e ET Chapter 4. All Answers (All)
Stewart - Calculus 8e ET Chapter 4. All Answers

1. Find the local and absolute extreme values of the function on the given interval. , 2. Find all the critical numbers of the function. 3. Find the maximum and minimum points of the function. 4....

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 Calculus > QUESTIONS & ANSWERS > Stewart - Calculus 8e ET Chapter 5. All Answers (All)
Stewart - Calculus 8e ET Chapter 5. All Answers

1. The velocity graph of a braking car is shown. Use it to estimate to the nearest foot the distance traveled by the car while the brakes are applied. Use a left sum with n = 7. 2. Evaluate by inter...

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 Calculus > QUESTIONS & ANSWERS > Stewart - Calculus 8e ET Chapter 6. All Answers (All)
Stewart - Calculus 8e ET Chapter 6. All Answers

1. Racing cars driven by Chris and Kelly are side by side at the start of a race. The table shows the velocities of each car (in miles per hour) during the first ten seconds of the race. Use the Midp...

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