Question of the Day
Posted on28 Dec 2020
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Prove that $\sqrt{2}+\sqrt{3}$ is irrational without assuming any particular surd is irrational i.e. you must prove first that a surd like $\sqrt{6}$... Read More
Question of the Day
Posted on27 Dec 2020
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Prove that cubic equations (of real coefficients) must have at least one real root.
Question of the Day
Posted on26 Dec 2020
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Find the region of convergence for the Taylor Series of $\ln(1+x)$ expanded at $x_0=0$.
Question of the Day
Posted on25 Dec 2020
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Find the region of convergence for the Taylor Series of $\frac{1}{1+x}$ expanded at $x_0=0$.
Question of the Day
Posted on24 Dec 2020
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Does the following converge or diverge? $\int_{0}^{3} x^{-\frac{2}{3}} dx$
Question of the Day
Posted on23 Dec 2020
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Does the following converge or diverge? $\int_{1}^{\infty} x^{-\frac{2}{3}} dx$
Question of the Day
Posted on22 Dec 2020
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Does the following converge or diverge? $\int_{0}^{3} x^{-\frac{3}{2}} dx$
Question of the Day
Posted on21 Dec 2020
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Does the following converge or diverge? $\int_{1}^{\infty} x^{-\frac{3}{2}} dx$
Question of the Day
Posted on20 Dec 2020
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Prove that the real numbers are not countable.
Question of the Day
Posted on19 Dec 2020
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Prove that if a function $f$ is bounded and monotonically decreasing on $[a,b]$ then it is Riemann-integrable on $[a,b]$.