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- integration - Evaluating $\int x^2 \sqrt {x^2-1} dx$ - Mathematics . . .
2 How do I evaluate the following indefinite integral? As a general rule, whenever evaluating an integral containing x2 ±a2− −−−−−√ x 2 ± a 2, one of the most natural substitutions is x = a cosh t x = a cosh t or x = a sinh t x = a sinh t, depending on the sign
- Evaluating $\\lim\\limits_{x\\to-3}\\frac{x^2-9}{2x^2+7x+3}$
The important thing to know at this level of evaluating limits is that if the numerator is zero, you can only conclude the whole thing is zero if the denominator is not zero We sometimes say 0 0 0 0 is indeterminate, because depending on how one gets to this symbolic expression 0 0 0 0, the actual limit may be any real number (or even±∞ ±
- Evaluating $ \\lim_{x \\to 0} \\frac{e - (1 + 2x)^{1 2x}}{x} $ without . . .
Evaluating limx→0 e−(1+2x)1 2x x lim x → 0 e (1 + 2 x) 1 2 x x without using any expansion series [closed] Ask Question Asked 10 months ago Modified 9 months ago
- algebra precalculus - Evaluating $\frac {1} {a^ {2025}}+\frac {1} {b . . .
You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
- Evaluating $\\int_0^\\infty \\sin x^2\\, dx$ with real methods?
Evaluating ∫∞ 0 sin x2 dx ∫ 0 ∞ sin x 2 d x with real methods? Ask Question Asked 12 years, 10 months ago Modified 5 months ago
- limits - Evaluating $\lim\limits_ {n \to \infty} ( (n^3 + n^2 + n + 1 . . .
Are you familiar with evaluating limits of the form x for ? If so, can you transform the given limit into the form above? – sudeep5221 Oct 20, 2023 at 18:33 @sudeep5221 I'm afraid I don't If were an integer, I would try to use the binomial theorem, but it seems that it can be an arbitrary positive real number
- Evaluating $\\int_{0}^{\\infty}\\frac{\\arctan (a\\sin^2x)}{x^2}dx$
Evaluating ∫∞ 0 arctan(a sin2 x) x2 dx ∫ 0 ∞ arctan (a sin 2 x) x 2 d x Ask Question Asked 12 years, 11 months ago Modified 6 months ago
- sequences and series - Evaluating $\sum_ {n=1}^ {\infty} 1 \phi (n)^2 . . .
Wolfram Alpha gives $$\sum_ {n=1}^ {10000} 1 \phi (n)^2\approx 3 3901989747265619591157$$ and a graph of partial sums indicates fairly clearly this converges: It's well-known that the sum of the inv
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