Chapter 4, Problem 238. The typesetting makes the problem ambiguous.
Chapter 4, Problem 320. A bit ambiguous. Better: Using the river as one side of the pen (because hogs never swim?), … .
Chapter 4, Problem 316. The cardboard (from which the box is to be made) has dimensions 2 by 4.
The definition of vertical asymptote (page 149 (157) needs one more or . Or better still just one of the one-sided limits is either plus or minus infinity.
Chapter 1, Problems 264-269 refer to vertical asymptote, but it seems that term is not defined until Chapter 2.
Chapter 4, Problem 39. The units in the answer should be miles per minute.
Chapter 4, Problem 207. In the answer, it is assumed that \( f^\prime \) is symmetric about the origin; In that case, \( f(2)-f(-2) = \int f^\prime(x) =0;\) and from examining the graph, \( f(x) = \int_{-2}^x f^\prime(t)\, dt >0, \ \ -2<t<2.\) In this way one sees that f attains its minimum at the end points. Also, the instructions should ask for locations of local maxima and minima.
The statement of the first derivative test needs revising. One option: Begin with Suppose f is continuous on an open interval \( I, \, c\in I\) is a critical point of f and f is differentiable on I, except possibly at c. i. If \( f^\prime \,\dots \, .\). The function \( f(x) = x^2 \sin^2(\frac{1}{x})\) for \( x\ne 0\) and \( f(0)=0\) and the point c=0 is a counterexample to the exactly one of the three options given must hold. Namely, the derivative of this function does not have constant sign in any interval of the form \( (0,a)\) (for a positive). In this example, the function is even differentiable at the critical point c=0; and achieves its (global) minimum at c=0.
Chapter 4. The instructions for problems 84 to 86 are a mess. In problem 85 there is not even a pretense of a need for calculus.
Chapter 4. The instructions for problems read simply Find. Note that dV is not the change in the volume; and none of the problems involve surface area.
Chapter 4, Problem 79. The solution should read \( 3x^2\, dx.\)
Chapter 4, Checkpoint problem 4.5 and problems 50-67 are dangerous. Since no error estimates (say like a verions of Taylor’s remainder formula) are established (or used), how is one to know their proposed estimate is accurate to within a specified amount? Also, replace the appropriate with appropriate in the instructions for those problems.
Chapter 5, Problem 159. The upper limit of integration should be (to match the answer given later) \( e^{x}\) or the answer should be 0.
Chapter 5, Problem 423. Change \( e^x \) to \(e^t. \)
Chapter 5, Problem 393. To match the answer given in the solutions, delete the square root sign from the integrand.
Page 608 (616). Equation (5.25) is broken. There are a number of possible fixes; e.g., add \( u >|a|>0 \).
Chapter 5, the instructions for problems 417-422 are nonsensical since one cannot speak of the antiderivative. Ditto for problems 407-410.
Bottom of page 608 (616), \( cos(y) = \sqrt{1-\sin^2(y)}.\)
Chapter 5, Problem 316, The substitution \( x= -\cos(t)\) is more convenient. The integral is easily computed (similar to early problems in the text) by interpreting it as representing the area of the upper half of the circle centered to the the origin with radius 1.
Chapter 5, Problem 343 should read \( \int x^2 \ln(x^2) dx.\) The answer should start with 2/9 and not 1/9.
Chapter 5, Problem 340 is ridiculous.
Chapter 5, Problem 342. The hint is wrong, but also not needed given the instructions preceding the problem.
Chapter 5, Problem 268. \( u= x^3-3x^2.\)
Section 5.4. The instructions for Problems 211 and 212 are nonsense.
The solution to Problem 277 Chapter 3 should be \(\frac{-1}{13}.\)
The solution to Problem 263 Chapter 3. Just wow. Who would guess the reciprocal of the square root of 3. Secretly it is assumed that the graph pictured is that of \( x^2+y^2=4\).
The solution to Problem 261 of Chapter 3 is not right. The graph pictured is not the same as in the problem.
Page 497 (505). Problem 500 is ok; but there is the subtlety that f is not differentiable at 0.
Page 497 (505). The instructions for problems 470-489 should read Find all antiderivatives (or the indefinite integral) of the following functions f.
Page 485. The antiderivative should read An antiderivative
Page 388. The instructions for Problems 161-166 are nonsensical.
Page 376 (384). Replace prove your hypothesis with support your hypothesis.
Page 352. Problem 361. New York and US appear to be used interchangeably.
Page 360. Problem 360. First use of the term half-life.
Page 327. Equation (3.35). \(g^{\prime\prime}\) should be \(g^\prime.\)
Page 318. Problem 325. x=4 and y=16 does not give volume 85, but rather 256/3.
Page 317. Problem 317. Normal has not been defined.
Page 287 (305). Problem 219. The derivative of the square root has not yet been presented. While one could compute this derivative from first principles, I don’t believe that was intended.
Page 285. Problem 189. A comma is missing.
Page 275. Problem 167. Best-fit has not been defined/introduced.
Page 264. Problems 119 and 136. The derivative of \( x^{frac23}\) has not yet been presented. While one could compute this derivative from first principles, I don’t believe that was intended.
Page 232. Open set is not defined.
Page 230. Problem 44. Not sure what is intended here, since f is not defined at 0.
Page 228. Problems 1-10. The instructions should read: Find the slope of the secant line using the formula \( \frac{f(x_2)-f(x_1)}{x_2-x_1}\).
Page 192. Problems 157,158. Replace the with a.
Page 187. The claim ultimately allows us … their domains is dangerously misleading. All that is needed is a trivial special case of Theorem 2.9.
Page 172. Last line. The argument is decidedly more involved than indicated. In figure 2.30, the area of the triangle with vertices (0,0),(1,0) and \((cos(\theta),\sin(\theta))\) is less than the area of the sector of the unit disc determined by \(\theta\) is less than the area of the triangle with (0,0),(1,0) and \((1,\tan(\theta))\); that is \( \frac{\sin{\theta}}{2} < \frac{\theta}{2\pi} \, \pi < \frac{\tan(\theta)}{2}.\)
Section 1.1. Given rules f and g, the domains are implicit – the set of real numbers for which the formula makes sense. Now when composing f and g, what is the domain supposed to be? For \( h=f\circ g\) one needs the range of g to lie in the domain of f. Accordingly, one might need to adjust the domain of g. On the other hand, one could consider the (formal) rule h with its implicit domain.
Page 19. The definition of increasing is not consistent with later usage (particularly in the problems); that is, in the problems it seems that increasing is taken to mean strictly increasing.
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