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I know that $\\infty/\\infty$ is not generally defined I know that there is a trig identity for $\cos (a+b)$ and an identity for $\cos (2a)$, but is there an identity for $\cos (ab)$ However, if we have 2 equal infinities divided by each other, would it be 1

Does anyone have a recommendation for a book to use for the self study of real analysis I only ask because i'm working a problem with a percent. Several years ago when i completed about half a semester of real analysis i, the instructor used introducti.

HINT: You want that last expression to turn out to be $\big (1+2+\ldots+k+ (k+1)\big)^2$, so you want $ (k+1)^3$ to be equal to the difference $$\big (1+2+\ldots+k+ (k+1)\big)^2- (1+2+\ldots+k)^2\;.$$ That’s a difference of two squares, so you can factor it as $$ (k+1)\Big (2 (1+2+\ldots+k)+ (k+1)\Big)\;.\tag {1}$$ To show that $ (1)$ is just a fancy way of writing $ (k+1)^3$, you need to ...

The theorem that $\binom {n} {k} = \frac {n!} {k Otherwise this would be restricted to $0 <k < n$ A reason that we do define $0!$ to be $1$ is so that we can cover those edge cases with the same formula, instead of having to treat them separately We treat binomial coefficients like $\binom.

I made up some integrals to do for fun, and i had a real problem with this one I've since found out that there's no solution in terms of elementary functions, but when i attempt to integrate it, i. I don't understand what's happening I tried solving the integral using integr.

Which definition of parabola are you using

The conic section one or the locus one If you use the second, you can derive the equation of the parabola and the coordinates of the vertex directly from it. Nietzsche recalls the story that socrates says that 'he has been a long time sick', meaning that life itself is a sickness Nietszche accuses him of being a sick man, a man against the instincts of.

Basically, what is the difference between $1000\\times1.03$ and $1000/.97$ For some reason i feel like both should result in the same number

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