# term

1. ### Estimating integral using Taylor Series, extra term

Hi I have a question to find the Taylor Series for y(x)=ln(1+x) up to and including terms of 0(x^5). I found that series to be: x - 1/2x^(2) + 1/3x^(3) - 1/4x^(4) + 1/5x^(5)...which may or may not be correct! The next part of the question asks: "Use the series to estimate the value of the...
2. ### Second Order ODE second term tending to 0 - question reads something must be unsolve

Hi, I have a 2nd order ODE of general form: y= Ae^(17x) + Be^(-x) Initial conditions are: y(0)=0; and y'(0)=2 From this I got A = 1/9 and B= -1/9 Leading to: 1/9e^(17x) - 1/9e^(-x) Even I can see the second term is tending to zero - as it was when I tested a few points. In the question...
3. ### Finding Ratios and First Term of Geometric Sums

Three integers x, y, and z (where x <= y <= z) form a geometric series with a common ratio r (which is also an integer). Given x + y + z = 741, what is the sum of all possible values of z? (Ans Key: 4870) I started doing some guess and check with my calculator and got z values of 247, 513, and...
4. ### Expanding a binomial and finding a specific term.

1) expand binomial (x-2y)^4 I got x^4+4x^3-2y+6x^2-2y^2+4x-2y^3-2y^4 Also is there any easier way to do this? I am using the binomial theorem, and it is hard to memorize all the formula. 2) (4x+3y)^10 Fidning term containing y^7 (210(4x^4)(3y^6))
5. ### Can someone explain me the term 6.5/1.2?

From where it comes from?
6. ### dominate term in numerator

still working an Analysis and have to say its not an area of mathematics that i am fond of (Headbang). The people at MHF have been my saving light(Bow)(Bow) Any who im still working on determining if sequences converge or not given the following can someone tell me if i am on the right track...
7. ### rotate the axes to eliminate the xy term?

Given x2-4xy+4y2+(5*sqrt(5))y+1=0 what are the steps to rotating this to eliminate the xy term? Thank you!
8. ### Finding a specific solution for a general term in a sequence and a general strategy

A problem says to: Write the nth general term of the following sequence: 1, 16, 243, 4096, and 78,125......etc The answer given is n(2+n) Is that the correct answer? Also, what is a general strategy for solving such problems? Is there anything better than just guessing a pattern?(Doh)
9. ### question about finding a term in a geometric sequence

A problem asks to find S6 for a geometric sequence starting with 4 with a common ratio 2. The answer given is: 252 I thought use the equation: an = a1 * r(n-1) so: an = 4 * 2(6-1) .....but this appears wrong according to the answer. Can someone help? (Headbang)
10. ### Finding a large term in an arithmetic sequence

A problem asks to find the 204th term of an arithmetic sequence with fourth term 8 and sixth term 36. The answer given is: 808 However, I'm not clear how that is determined. I though the equation to determine a term was an = a1 + (n-1)*d
11. ### nth Term of Sequence

I would appreciate someone's help. I am trying to find the nth term of the following sequence: -1, 5, -17, 65....
12. ### how to solve fractions with an algebraic term

Hi, guys I need some help to properly solve this value. I'm currently learning Elementary Algebra. So far it's exciting, but I'm having hard time to solve this equation for X. The question explains here in the book: Find the value of \frac{2 + 0.15x}{x} for each of the values of x given...
13. ### Close form solution to minimize norm of quadratic term

For a problem I am working on I need to minimimize \sum_t || x^TA_tx - b_t||^2_2, with respect to x \in R^n. The matrix A_t \in R^{n \times n} is not positive definite, b_t \in R. Is there a closed form solution for this? The norm can also be the L1 norm and does not need to be squared, if...
14. ### Term deposit interest calculation.

Hi, I've been struggling with this problem for days now. It seems really simple, but I'm having issues. Here's the problem: Bob gets paid fortnightly. He wants to save 6000 dollars in 1 year. His savings account offers 5 percent interest for 3 months maturity with a minimum of \$2000 term...
15. ### general solution of differential equation (express y in term of x)

i got stucked here. below is the answer given. can anybody help please?
16. ### Phase Line and long term behavior with initial value

Ok so i have the equation y'=y^2(y-3)(y-5)^3 I found the equilibrium positions to be y=0, y=3, y=5. Does my phase diagram look right and would be correct in saying the solutions are nodes? The last part asks Describe the long term behavior of the solution to the above dierential...
17. ### Phase Line and long term behavior with initial value

Ok so i have the equation y'=y^2(y-3)(y-5)^3 I found the equilibrium positions to be y=0, y=3, y=5. Does my phase diagram look right and would be correct in saying the solutions are nodes? The last part asks Describe the long term behavior of the solution to the above dierential...
18. ### general term in tan x series

I can't find anywhere what the general term is in the series for tan x. The denominator appears to be (2n+1)! The degree of x is (2n+1).
19. ### How to solve a quadratic which has a term with a square root over the variable?

How to solve a quadratic which has a term with a square root over the variable?
20. ### Reducing variable to 1 term: simplifying a fraction

Hi there, I have an equation P(x) that resembles: (C1e-ax + C2e-bx) (e-ax + e-bx) where the horizontal line represents a division line. I do not know the values of a, b or C1 nor C2​, but they all have the same units. I am supposed to graph P as a function of x, for which I assume I need to...