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- Polar Coordinates as a Definitive Technique for Evaluating Limits
A lot of questions say "use polar coordinates" to calculate limits when they approach 0 0 But is using polar coordinates the best way to evaluate limits, moreover, prove that they exist? Do they account for every single possible direction to approach a limit, for example, along a parabola Specifically, if I were to show that
- Easy way to compute logarithms without a calculator?
I would need to be able to compute logarithms without using a calculator, just on paper The result should be a fraction so it is the most accurate For example I have seen this in math class calc
- Evaluating $ \\lim\\limits_{n\\to\\infty} \\sum_{k=1}^{n^2} \\frac{n}{n . . .
How would you evaluate the following series? $$\\lim_{n\\to\\infty} \\sum_{k=1}^{n^2} \\frac{n}{n^2+k^2} $$ Thanks
- Determine the sign of an integral without evaluating it
You know by symmetry the integral would be 0 if the integrand was cos(x) cos (x) What is the sign of cos(x) cos (x) when the x x affects the magnitude the most? You are correct in splitting it into partial integrals, but which one logically should be larger? When is x x larger?
- Is there a way to get trig functions without a calculator?
In school, we just started learning about trigonometry, and I was wondering: is there a way to find the sine, cosine, tangent, cosecant, secant, and cotangent of a single angle without using a calc
- Show that $\\det(A) = 0$ without directly evaluating the determinant
Show that det(A) = 0 det (A) = 0 without directly evaluating the determinant Ask Question Asked 7 years, 8 months ago Modified 7 years, 8 months ago
- limits - Evaluating $\lim_ {x\to 0}\frac {e^x+e^ {-x}-2} {1-\cos x . . .
Compute without using L'Hospital's Rule $$\\lim_{x\\to 0}\\dfrac{e^x+e^{-x}-2}{1-\\cos x} $$ I thought of simplifying the limit as shown below \\begin{align} \\lim
- Evaluating $\\sum_{r=1}^n \\frac{\\tan(x 2^r)}{2^{r-1}\\cos(x 2^{r-1})}$
I proceeded by breaking tan x tan x into sin x sin x and cos x cos x and writing numerator as follows
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