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### Typos in Princeton Review

Posted: Sun Jun 30, 2013 12:32 am
I have found many typos and looked for a list somewhere to no avail. So here is mine. This will be updated often as I finish more of the book. I cover sections randomly so these will be done in no particular order.

Page 6, line -10: "is" should be "as".
Page 8, example 1.5: "on A" should be "from A to R".
Page 27, line 11: ">=" should be "<=".
Page 33, example 19: Choice (D) should have a + before the radical, not a -.
Page 33, example 21: Remove "and 2 < x < 3" as this information is unnecessary.
Page 39, line 6: Insert a delta symbol after "number".
Page 39, last line: The last limit should be as x approaches 1, not as x approaches one from the left.
Page 43, line -11: "q - 1" on the left of the equality should be "q - 2" and "q" on the right of the equality should be "q - 2".
Page 43, line -9: Delete "the".
Page 43, line -8: "(a - r, a + r)" should be "(a - /delta, a + /delta)".
Page 49, last line: "opposite" should be "negative".
Page 52, line 4: The symbol between x and 1/x should be a multiplication operator.
Page 62, line 16: The last cos(theta) should be in absolute values.
Page 70, line 3: The upper limit of integration should be raised to the top of the integral sign and the integral sign slightly lowered.
Page 76, line 5: The last radical should have (dx/dy)^2 inside, not (dy/dx)^2.
Page 80, solution (C): Remove the second term in the chain and also remove the x in the third term of the chain.
Page 98, problem 21: The interval should be (0, pi/2), not (0, 3pi/2).
Page 108, line -11: "associative" should be "distributive".
Page 110, line 3: "opposite" should be "negative" and "associative" should be "distributive".
Page 118, line -5: "x^(2/9)" should be "z^2/9".
Page 126, line 7: Delete "assuming that f_x and f_y aren't both equal to zero at P."
Page 126, line 13: Delete "assuming once again that dz/dx and dz/dy aren't both equal to zero at P."
Page 135, line 12: Insert "not defined or" before "both".
Page 137, line 19: "on the top edge, but not withinin" should be "is not in".
Page 148, line 7: The closed integral should be a regular integral.
Page 148, line 12: The closed integral should be a regular integral.
Page 150, lines -2, -1: "on the next page" should be "as shown below".
Page 150, graph: Delete "exits at x = /radical y", delete "exits at x = 2", and delete the horizontal line.
Page 169, line -1: Change the absolute value symbols to parentheses.
Page 172, line 12: The last "x" should be "|x|".
Page 172, line 15: The last "x" should be "|x|".
Page 198, line -12 and -11: Rm and Rn should be R^m and R^n.
Page 209, line 4: "S" should be "Theorem".
Page 222, line 11 and 12: "23" should be "2^3", "70" should be "7^0", "110" should be "11^0", "25" should be "2^5", and "32"should be "3^2".
Page 227, line -2: The approximation sign should be an equality.
Page 237, line 16: Insert "has" before "order n".
Page 239, line 12: Insert "2," before "2,2,3,5,5".
Page 240, line -8: "also has order" should be "has order that divides".
Page 242, line 12: "phi(1)" should be 3 x phi(1)".
Page 249, line -1: "R`" should be "R".
Page 258: The second and third row of the ~X and ~Y columns should be F T and F T, not T F and T F.
Page 263, line 5: "on the previous page" should be "above".
Page 274, line 13: Insert a colon after "S".
Page 276, line -8: "0.16" should be "0.20".
Page 288, line 21: "[0,1]" should be '[0,1]->".
Page 300, last line: Remove the S in the first exponent.
Page 302, line 5: "2pi" should be "2pi*i" in the second expression in the chain.
Page 308, line -6: The last terms should be "2z".
Page 318, line 6: "39" should be "59".
Page 318, line 7: "275" should be "576".
Page 320, problem 10: The denominator of (A) should be g^(n), not, g^n.
Page 320, problem 10: All 10 numerators and denominators should be evaluated at x_n, not x.
Page 321, problem 14: "expansions" should be "expansion".
Page 324, problem 26: v, (C), and (D) should all have 3x^(2y) changed to 3(x^2)y.
Page 325, problem 30: (D) should have the 2^6() at the end deleted.
Page 325, problem 31: (B) should have commas instead of ampersands.
Page 325, problem 32: f(x) is nonzero from when x (not t) is 0 to 6, not 0 to 8.
Page 327, problem 38: F_X should be 2/(3^t) and F_Y should be 3/(4^t).
Page 328, problem 44: The coin should be tossed 100 times, not 10 times.
Page 328, problem 46: Remove the first i in (A), the second i in (C), and the second i in (E).
Page 336, problem 19: "then" should be "and".
Page 339, problem 3: The first limit in the third line of the problem should be as x approaches negative n from the left, not n.
Page 343, problem 15: "all x" should be "x /epsilon [-1,1]".
Page 345, problem 21, line -8: "0 < x < 3pi/2" should be "0 < x < pi/2".
Page 359, problem 47, lines -5 to -2: 5 of the minus signs are merged with the fraction symbols.
Page 361, problem 50, line 7: "7/480" should be "1/160".
Page 361, problem 50, line 11: "7/480" should be "1/160" and "1/144" should be "1/160".
Page 389, problem 5, line 5: "25" should be "5".
Page 390, problem 14, line -1: "{0,4,5}" should be {0,3}".
Page 395, problem 14: The correct answer is D, as each summation should be from 0 to infinity, not 1 to infinity.
Page 397, problem 22: g(A) = J, g(B) = K, g(C) = L, g(D) = M.
Page 399, problem 30: The 5pi/6 that appears in two of the equations should be in the exponent.
Page 399, problem 31: "that" should be included after "theorem".
Page 399, problem 32: The upper limit of integration should be 6 and 64 should be 36.
Page 419, problem 62: Insert "subset" after "infinite" in answer (b).
Page 422, problem 6: line -7: Insert "and a_n > o" after "with n odd".
Page 427, problem 25: Insert absolute values around the log arguments in the first integral.
Page 433, problem 39: "(A) and (B)" should be "(A), (B), and (C)".
Page 434, problem 43: The first gradient in the third line should have no subscript.
Page 434, problem 43: The "thetas" in the first trigonometric identity should not overlap the cosines.
Page 443, problem 62: Insert "subset" after "infinite" in the last line.

### Re: Typos in Princeton Review

Posted: Fri Oct 04, 2013 1:15 pm
Well, I took the exam so no more studying for me...unless I need to do it again. Hence, this will probably be it for awhile even though I never finished the book.

### Re: Typos in Princeton Review

Posted: Sat Oct 05, 2013 2:19 am
Thank you so much for compiling this list! The review questions in the last chapter are absolutely wrought with errors!

### Re: Typos in Princeton Review

Posted: Thu Oct 17, 2013 10:46 am
Thanks for this! I will have to look this over in detail to see how it compares to mine (at last count I was up to 29 errors), but at first glance I saw one serious one that you missed. On p. 313, near the top, the conclusion that z=1 is an essential singularity is wrong. It is clearly a simple pole. The error the author makes is that he draws his conclusion from the fact the the Laurent series he just derived has infinitely many terms, but this only indicates an essential singularity if the series is centered at the singularity, which this one is not since it is centered at z=0. The Laurent series for the function 1/(1-z) centered at z=1 is just the function itself, which obviously has only one term and is therefore a simple pole. You could also see this by looking at the bottom of p. 311. Sine f(x) = 1/(1-z) is written in the form g(z)/(z-z0)^n, with z0=1, n=1, and g(z)=-1 which is analytic, it is a pole of order n=1 and therefore a simple pole. I consider this the most glaring error I have found to date because it is not just a "typo" but a conceptual mathematical error.

### Re: Typos in Princeton Review

Posted: Fri Oct 18, 2013 12:22 pm
I went through my notes and added the remaining corrections I found.

Here are the pages I never got to (including 313!):

289-298
310-315
377-387

There were some other sporadic pages I never "completed" as I was working through the math and never got around to finishing.

### Re: Typos in Princeton Review

Posted: Fri Oct 18, 2013 8:15 pm
Really useful list. Thanks for compiling this.