Recent content by BreCheese

I can't recall learning much about the complex plane. My math experience is only up through Calc 2 (I'm 3/4 of the way through completion of college Calc 2). What level of mathematics did you learn in depth about the complex plane that you're referring to?

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Because the hypotenuse becomes the proceeding triangle's shortest leg, and because we were given the expression of the longest leg. I thought that I'd use trigonometry to define the angle: tanθ=((2^(n-1)) / (root((4^(n-1)+2) / 3)) ; where the numerator is the expression for the longest legs, and...

Thank you both so much for your help! I appreciate it greatly :) Below is what I came up with. However, the challenge now is finding the limit properly, instead of just observing the expansion of the sequence expression...

Homework Statement I need to mathematically prove that the center angle(s) (labeled as "A" in the photo below) approach what I believe to be 60 degrees (but never reach 60 degrees). We are given the values of all longer legs of each right triangle. Furthermore, the value of the length of each...

This formula is intuitive and really drives home what a derivative actually is. Thanks for sharing it. f(x) - f(a) is really a fancy way of saying change of y, denoted as Δy, or in other words, y2 - y1. Similarly, x - a is a fancy way of writing change in x, denoted Δx, or in other words x2 -...

To tell which function is "the upper curve" or "lower curve" you can choose any value of x (provided that your choice of x is in the interval of interest) and evaluate each function at that x value to determine which function is the upper (or lower) curve. The upper curve will be the function...

A degree can be broken into even smaller measurements, much like a foot can be broken down into inches, and say, centimeters. One practical reason we break a degree into even smaller parts is so we can accurately measure the nautical space between distant objects in deep space. I don't have a...

I first taught myself to recognize and name series (geometric series, telescoping series, harmonic series, p-series, alternating series, etc). All of these series have their own set of conditions and rules to follow, so it is difficult to identify which series you're looking at at first (but...

I posted two photos below showing how to determine convergence or divergence. The first photo proves why the divergence test is inconclusive for the series you provided. The second photo shows how to prove divergence of the series you provided by means of the integral test. Hope this helps. Let...

Furthermore, we can NOT say that if the limit of a sub k (as k tends to infinity) equals zero, then the infinite series converges. Hence, the divergence test only tests for divergence of an infinite series, and is thus inconclusive when considering convergence behavior of a given infinite series...

Interesting question! My professor opened up his lecture about the divergence test by introducing logic concepts. For instance, the divergence test states that If the series a sub k converges, then the limit of a sub k (as k tends to infinity) equals zero. If we label the premise, A, "the...

If you have the Δx, or as you put it, the "step" you don't need "n" to calculate the area using the trapezoidal rule. in short, Δx=(b-a)/n. The trapezoidal rule is as follows Δx[½f(x0)+f(x1)+f(x2)+...+f(xn-1)+½f(xn)] ; where 0, 1, 2, n-1, n are subscripts of x (I just don't know how to use...

I don't see a substitution, or perhaps I don't understand your question What your professor did is apply the power rule, which states that if y=x^n, then y'=nx^(n-1) So in your particular problem this is the step-by-step way to get the derivative: x=1/z x=z^(-1) dx/dz=(-1)z^(-1-1) ; read, the...

Ah, I think my kinematic equation is wrong, or rather, can not be applied for motion with constant acceleration in the y-direction.