Question of the Day
Posted on18 Nov 2020
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Calculate the limit \lim\limits_{x \to 0 } x \ln x without using L’Hôpital’s rule.
Question of the Day
Posted on17 Nov 2020
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Does the following converge or diverge? $\int_{0}^{1} \ln x dx$
Question of the Day
Posted on16 Nov 2020
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Does the following converge or diverge? $\int_{0}^{1} x^{-1} dx$
Question of the Day
Posted on15 Nov 2020
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Does the following converge or diverge? $\int_{0}^{1} x^{-\frac{1}{2}} dx$
Question of the Day
Posted on14 Nov 2020
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With the help of Rolle’s Theorem and the function $f\left(x\right)=e^{-x} \left(x-a\right)\left(x-b\right)$ prove that the equation $\left(x-a\right)\left(x-b)=\left(x-a\left)+\left(x-b\right)$ will have a solution in the... Read More
Question of the Day
Posted on13 Nov 2020
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Does the following converge or diverge? $\int_{0}^{\infty} e^{-x} dx$
Question of the Day
Posted on12 Nov 2020
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Prove that polynomials with real coefficients and odd degree always have at least one real root.
Question of the Day
Posted on11 Nov 2020
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Find the Maclaurin Series of $\frac{4x^2-3}{\left(1-x\right)\left(1-2x\right)^2}$ where $x$ is small i.e. less than $\frac{1}{2}$ in magnitude. But, you can’t use the formula... Read More
Question of the Day
Posted on10 Nov 2020
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Find a cubic approximation for the $\tan x$ when $x$ is small, i.e. $|x|<\frac{\pi}{2}$.
Question of the Day
Posted on09 Nov 2020
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Find the Taylor Series of $\frac{1}{\left(1-x\right)^2}$