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Advanced Math/Questions Answered by Expert Socrates
| Subject | Date Asked |
| convergence of series | 11/22/2011 |
| Q: How do you prove by comparison test that n!/(n^3) converges or diverges? A: Compare n!/n^3 to 1/n n!/n^3 > 1/n (n-1)!/n^2 > 1/n (n-1)!/n > 1 (n-2)! (n-1)/n > 1 Since ... | |
| algebra | 9/18/2011 |
| Q: 1.find the polynomial function of least degree with integral coefficient which has 2-squareroot of 3 ... A: 1) Since complex zeros for polynomials with real coefficients always occur in conjugate pairs, 1+i ... | |
| Are My Answers Correct? | 8/19/2011 |
| Q: I was wondering if you could clarify whether or not my answers are correct. I don't want to turn ... A: The first two are ok. Look what you have sent me for the third problem: "Now, on Problem 3, I need ... | |
| Find the length of an arc | 7/18/2011 |
| Q: 1.r=17.2in, θ= π/3 3.r=12.78in,θ= 72° 5.s=5.0 m,r=20.0 m 7.s=36.8 yd,r=23.4 yd i ... A: s=rθ , where θ is the radian measure of the angle , r is the radius and s is the arc ... | |
| Pure maths | 10/27/2010 |
| Q: The figure shows the curve with the equation y=-2x^2+6X-4. The curve meets the y-axis at the point A ... A: To find C we want the zeros of y=-2x^2+6X-4. Solving 0 = -2x^2+6X-4 , we get x=1 or x=2 , so ... | |
| Parabolas | 10/26/2010 |
| Q: A travel agency offers an organization an all-inclusive tour for $800 per person if 100 persons or ... A: Let x be the number of people taking the tour. Let R(x) be the revenue. If x<= 100 , R(x) = 800x ... | |
| Vectors | 7/27/2010 |
| Q: The problem is written with diagram in the picture attached. I've been working on this problem for ... A: |CE| = (2/5)|CB| , so the vector CE is (2/5)(B-C) |AD| = (2/3)|AB| , so the vector AD is (2/3)(B-A) ... | |
| Probability | 12/3/2009 |
| Q: A letter is known to have come from either TATNAGAR or CALCUTTA. on the envelope just two ... A: i) In TATANAGAR there 8 possible two letter consecutive sequences (TA, AT, TA, AN, NA, AG, GA, AR) ... | |
| My answers don't match up with the textbook | 12/2/2009 |
| Q: Struggling with algebra: difference quotient specifically: f(x) = x^2 - x + 1 f(x + h) - f(2)/h The ... A: I assume you mean (f(2 + h) - f(2))/h f(2+h) = (2+h)^2 - (2+h) + 1 = (4 + 4h + h^2)- (2+h) + 1 ... | |
| help me.... please | 12/1/2009 |
| Q: in school i am ahead in my math class so the teacher will usually give me more advanced work on the ... A: 0^0 is not defined to be 1 , there is no good way to define 0^0 . Mathematicians leave it undefined. ... | |
| Advanced Math | 11/30/2009 |
| Q: I have a question for Trig Identities. I need to prove the Identity (cosx / sec x -1) - (cosx / ... A: cosx/(secx - 1) - cosx/(secx + 1) multiply numerator and denominator of both fractions by cosx = ... | |
| Mathematical Expression | 9/30/2009 |
| Q: How can a situation be reduced to or expressed as the following: $1.50, per person, per day? Would ... A: $15 for 10 people for 10 days would work out to .15 per person per day , so that's not right $150 ... | |
| Family of functions? | 8/27/2009 |
| Q: Here's my question. Consider the family of functions: Fn(x) = x + 4x^2 + 9x^3 + ... + n^2*x^n x = ... A: " x + x^2 + x^3 + ....+ x^n approaches x/(1-x)" x + x^2 + x^3 + ....+ x^n + ..... is a geometric ... | |
| Family of functions? | 8/26/2009 |
| Q: Here's my question. Consider the family of functions: Fn(x) = x + 4x^2 + 9x^3 + ... + n^2*x^n x = ... A: (Fn(x))/x = 1 + 4x + 9x^2 + ....+ (n^2) (x^(n-1)) = (x + 2x^2 + 3x^3 +....+ nx^n)' = ((x)( 1 + 2x ... | |
| Precalculus | 7/22/2009 |
| Q: 1+sec A/sec A = sin^2/1-cos A establish an identity...i got all the work, but some where im doing ... A: Your work is correct as far as it goes. The left side is cos A + 1 , as you have found . But the ... | |
| math | 5/21/2009 |
| Q: Find the algebraic sum of the following: (2a+3b)/3a - (a-2b)/4b + (a^2+b^2)/ab A: The common denominator is 12ab (2a+3b)/3a = (4b)(2a+3b)/12ab = (8ab + 12b^2)/12ab (a-2b)/4b = ... | |
| exponential question | 8/21/2008 |
| Q: I am having a problem solving this equation for x: y = a ---------- -((x-c)/b) 1+ e ... A: take the reciprocal of both sides and get 1/y = (1/a)(1+e^-((x-c)/b)) multiply both sides by a ... | |
| nth Series formula | 6/21/2008 |
| Q: ,4,16,256...........please let me know how to find the nth term of this series. - Hide quoted text - ... A: 4 = 2^2 16 = 4^2 = 2^4 256 = 16^2 = 2^8 Each term is the square of the one before. This means that ... | |
| average rate of change | 5/21/2008 |
| Q: I am working on this practice problem Water usage rate for a city in a given 24-hour time period is ... A: a) 27.8 million gallons From t=0 to t=2 , the average rate of water use is (.5+.6)/2 =.55 million ... | |
| trigonometry | 2/21/2008 |
| Q: Solve the equation for theta: sec(theta + 10degrees)= csc(2theta + 20degrees) Any help is greatly ... A: I will use "t" for the angle theta sec(t+10) = 1/cos(t+10) csc(2t+20) = 1/sin(2t+20) Use the ... | |
| calculus | 10/22/2007 |
| Q: am having a little trouble understanding some of the ways to solve limits by differentiation. this ... A: I think you wanted lim (1+1/x)^x , since the limit you have asked for is clearly 1 , without using ... | |
| Antidifferentiation | 7/21/2007 |
| Q: I would be really extremely grateful for some help on this problem. I have a huge equation with big ... A: First , do some algebra to combine the constant terms . Next, make a change of variable to eliminate ... | |
| Pre-calculus | 5/15/2007 |
| Q: I need some help, I have no idea how to do this. 1 - cos2x sec(squared)x = tan(squared)x a "hint" ... A: use cos(2x) = cos^2(x) - sin^2(x) and sec^2(x) = 1/cos^2(x) substitute these into the left side and ... | |
| Pre Calc | 12/12/2006 |
| Q: An open top box is to be constructed from a 6 in by 8 in rectangular sheet of tin by cutting out ... A: a) Length of box is 8 - 2x Width of box is 6 - 2x Depth of box is x Thus, the volume will be V ... | |
| Mathematics Extended Essay Topic | 11/19/2006 |
| Q: my name is Ahalya and I am currently enrolled in the IB Diploma Program (12th Grade). As part of our ... A: It is difficult for me to suggest a topic because I don't know how much mathematics you know. The ... | |
| Test Question Pre-calculus/related more to algebra | 9/27/2006 |
| Q: The square root of x-3 plus the square root of x =5 I figure the answer is no solution, but I ... A: (x-3)^1/2 + x^1/2 = 5 square both sides (x-3) + x + (2)(x-3)^1/2 x^1/2 = 25 simplify ... | |
| math | 9/26/2006 |
| Q: Divid 21 into 2 pats so that 5 times are pat added to twice the other pat makes 66 ? A: Let the parts be x and y. x+y = 21 Five times one part added to twice the other makes 66 , so 5x ... | |
| Simple Derivative | 8/24/2006 |
| Q: What is the derivative in respect to x of tan^(-1)x I don't believe this is very complicated. ... A: The answer is 1/(1+x^2) You can't use the rules for taking derivatives to get this directly, you ... | |
| combinations | 8/15/2006 |
| Q: I have 16 golfers. Can I divide them into 4 person groups so that over 4 days they will not play ... A: There are many ways to do this, if you need to know how many ways, I am not sure that I can answer. ... | |
| limits | 8/8/2006 |
| Q: how do i solve lim 1-x² x->1 ________ x²+5x-6 A: The problem with (1-x^2)/(x^2 + 5x - 6) is if you let x=1 , you get 0/0 , which is undefined and ... | |
| Vector notation | 7/27/2006 |
| Q: This is a simple question. I am studying mathematics on my own at the undergraduate level. Not ... A: As far as I know , there is not one single standard notation for vectors. The notation I see most ... | |
| Math | 5/17/2006 |
| Q: If two gloves and a one bat equals 130$ and three bats and one glove 130$ How much is one glove ... A: g = cost of glove b = cost of bat 2g + b = 130 g + 3b = 130 Multiply both sides of the second ... | |
| square roots | 2/7/2006 |
| Q: I'm confused is the square root of 4 always 2? -2? is the square root of x, x? -x also? I'm confused ... A: The square root of a number is always positive, the square root of 4 is +2. The square root of x ... | |
| derivatives on logarithms | 10/30/2005 |
| Q: find the derivatives of y with respect to x, t, or theta, as appropriate. 1) y= (1 + ln t)/(t) 2) ... A: 1) Use the quotient rule: y' = [(t)(1+lnt)' - (1+lnt)t']/t^2 y' = [ (t)(1/t) - (1+lnt)]/t^2 y' ... | |
| implicit differentiation | 10/29/2005 |
| Q: find dy/dx. 1) ln y=e^ysinx 2) e^2x=sin(x+3y) A: 1) y'/y =( y'sinx + ycosx) e^ysinx y' = (yy'sinx)(e^ysinx) + (y^2 cosx)(e^ysinx) ... | |
| zero in the denominator | 9/29/2005 |
| Q: Do you have a suggestion of how I can prove to my 8th grade Algebra I class that a zero in the ... A: I can think of two ways to try and show this. I will keep it as simple as I can. If your students ... | |
| differential equation | 9/28/2005 |
| Q: I'm trying to solve the DE: cos(x)dx + (1 + (2/y))sin(x)dy = 0 using an intergration factor I let ... A: First, the integrating factor really is (e^y)(y^2), as you found correctly. But, did you multiply ... | |
| small conversion question! | 9/27/2005 |
| Q: My name is Assaf and I have a question about conversion: I have to convert inches into: Yards, feet ... A: I don't know a simple formula for this , the only formula I know is complicated and uses the ... | |
| Find all the rational zeros... | 6/27/2005 |
| Q: Find all the rational zeros of g(x) = 2x^3 - 11x^2 + 8x + 21. A: Using the rational roots theorem, you check every possible factor of 21 divided by every possible ... | |
| limits | 5/27/2005 |
| Q: What is the limit of k/x as x approaches 0 from the left?WHy is it infinity not negative infinity? A: It depends on whether k is a positive or negative number. If k is a positive number, the limit will ... | |
| word problem | 9/27/2004 |
| Q: Here is a question from the Quantitative section of the GRE. Their word problems are mean and ... A: Let's find M. The cost of producing M hats will be $15,000 + $5M The revenue from selling the M hats ... | |
| help please | 1/24/2004 |
| Q: If three fair standard dice are tossed, what is the probability that the results will be three ... A: There are 6x6x6 = 216 possible outcomes when the three dice are tossed. The three consecutive ... | |
Advanced Math
Answers by Expert:
Socrates
Top Expert on this page
Expertise
I can answer any questions from the standard four semester Calulus sequence. Derivatives, partial derivatives, chain rule, single and multiple integrals, change of variable, sequences and series, vector integration (Green`s Theorem, Stokes, and Gauss) and applications. Pre-Calculus, Linear Algebra and Finite Math questions are also welcome.
Experience
Ph.D. in Mathematics and many years teaching undergraduate courses at three state universities.
Education/Credentials
B.S. , M.S. , Ph.D.
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