Mathematics

Show that lim n approaches infinity (1 + 1/2n)^n= square root of e

Need help with the proof of this please!-consider the quantity e^(ln f(n) ), where f(n) = (1+1/2n)^n Then the quantity becomes e^( n ln(1+1/2n) ), or e^( ln(1+s/2) / s), where we define s = 1/n We a

Integral Question e^(2x) dx / e^(2x) + 3e^x + +2

I have the answer book, dont understand how to get to one step [int] e^(2x) dx / e^(2x) + 3e^x + 2let u = e^x, then x = ln u and dx = du/u [int] u² * du/u / u² + 3u + 2 (one of the Us will cancel on t

Calculus integration problem

Hello everyone, I was doing the following problem: ∫ (1) / (9 +16x^2) dx I had to use inverse trigonometric functions to do the following integral. These are my steps: ∫ (1) / (16(9/16 + x^2)) dx (1/

Find f''(2) when f(x)=x^2/(4+x).

Use the quotient and product rules to solve.-f(x) = x²/(4+x) f(x) = [2x(4+x) - x²] / (4+x)² f(x) = (8x + 2x² - x²) / (x² + 8x + 16) f(x) = (x² + 8x) / (x² + 8x + 16) f(x) = [(2x+8)(x²+8x+16) - (2x+8)(

How would you factor this

3(x+5)^2+5(x-3)(x+5)-3(x+5)^2+5(x-3)(x+5) = (x+5) [ 3 (x+5) + 5 (x-3) ] = (x+5) [ 3x +15 + 5x - 15] =8x(x+5) answer-Given : 3(x+5)^2+5(x-3)(x+5) = (x+5) [ 3 (x+5) + 5 (x-3) ] = (x+5) [ 3x +15 + 5x - 1

Help on this algebra 1 story problem please I dont get these.

I dont understand how to lay out the problem so if you could explain that to me as well thanks! It would really help I have a test soon. Come up wit a problem and solve. Grandma gave some baseball ca

Calculus Help Please -Calculus 1-

Consider the function f(x) = 3(1 − e^x). (a) Find the exact slope of the graph of f(x) at the point where it crosses the x-axis. slope = (b) Find the exact equation of the tangent line to the graph

Math help with algebra please!

Math help with algebra please!? A Crate containing 36 grapefruit has a total mass of 10kg. Then 10 grapefruit are removed, the total mass is 8kg. Determine the mass of the crate and the mass of one gr

How to factor : x^3 - 4x^2 - 11x + 30? Step by step = 10 points

Using the Rational Root Theorem, possible rational roots include ± {1, 2, 3, 5, 6, 10, 15, 30}. Using Synthetic Division, I find that x = 2 is a zero, so (x - 2) is a factor. The remainder after div

Using Parallel Lines and Transversals: Challenge Question

http://library.thinkquest.org/20991/media/geo_tran.gif in the diagram, angle 4 would be 13y. angle 3 would be 8x + y, and angle 8 would be 10x + 3y. The rest is unknown. How do i find the angle measur

Question about graphing

So I have this problem, and whenever I do it I get a striaght line, but Im supposed to come up with a result of a V. Can someone explain it to me, heres my question: y = |x + 5| − 3 I used for X: -6

Show directly that any multiple of a Cauchy sequence is again a Cauchy sequence

Suppose {x_n} is Cauchy and c is a real constant. We need to show that {c*x_n} is Cauchy. If c = 0, then {c*x_n} is the zero sequence, which is trivially Cauchy since the absolute value of the differ

Find a vector parametric equation for the line through the points P= (0,4,-3) and Q=(-5,4,1)

For each of the given conditions on the parameter t: if r(0)= (0,4,-3) and r(2)=(-5,4,1) if the points p and q correspond to the parameter values t=0 and t=-4 Any help would be greatly appreciated.-v

Math Pros: The Circle Formula

Where did (x-h)^2+(y-k)^2=r^2 even come from? How was it created? Use of coordinate geometry? (I know its the internet and that you cant really show visuals-explain in words?)-The equation of a circ

There are 51 students in a certain class. The number of females is 5 less than three times the number of males

Let the no. of males be x. No. of females -> 3x - 5 3x - 5 + x = 51 4x - 5 = 51 4x = 56 x = 14 The number of males is 14. No. of females = 14 * 3 - 5 = 42 - 5 = 37 The number of females is 37 I h