List questions from substitution

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system of equations with 3 variables in denominator

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Given that $\lim \limits_{x \to 0} \dfrac{\sin x}{x}=1$ can we simply invoke that $\dfrac{\sin(0)}{0}=1$ in the absence of the limit notation?

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Minimum value of rational expression

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Limits with Taylor series

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Efficient way to compute the ninth order Maclaurin polynomial of $\sin(\arctan(x^2))$

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Find max value of $a$

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Solve the ODE : $(x\sin(y)+y\cos(y))dx+(x\cos(y)-y\sin(y))dy=0$

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156

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prove this inequality $Σ_{cyc}\frac{a^3+abc}{b^2+c^2}\ge a+b+c$

Published on 26 Mar 2026 - 21:25

38

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Understand the solving strategy for difference equations.

Published on 04 Jan 2018 - 16:42

165

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Show that $\frac{x^2}{(x-1)^2} + \frac{y^2}{(y-1)^2} + \frac{z^2}{(z-1)^2}\ge 1$ for real numbers $x$, $y$, and $z$ with $xyz=1$.

Published on 05 Jan 2018 - 0:15

List Question

Integrating $\int_{x_1}^{x_2}\sqrt{1+(2at-a(x_1+x_2))^2}\,dt$

system of equations with 3 variables in denominator

Given that $\lim \limits_{x \to 0} \dfrac{\sin x}{x}=1$ can we simply invoke that $\dfrac{\sin(0)}{0}=1$ in the absence of the limit notation?

Limit of $f(x)$ as $x \to 0^{+}$

Limit of $h(x)$ as $x \to \infty$

2nd solution of $\cos x \cos 2x\cos 3x= \frac 1 4 $

Minimum value of rational expression

Limits with Taylor series

Looking for antiderivative

Efficient way to compute the ninth order Maclaurin polynomial of $\sin(\arctan(x^2))$

Find max value of $a$

Solve the ODE : $(x\sin(y)+y\cos(y))dx+(x\cos(y)-y\sin(y))dy=0$

prove this inequality $Σ_{cyc}\frac{a^3+abc}{b^2+c^2}\ge a+b+c$

Understand the solving strategy for difference equations.

Show that $\frac{x^2}{(x-1)^2} + \frac{y^2}{(y-1)^2} + \frac{z^2}{(z-1)^2}\ge 1$ for real numbers $x$, $y$, and $z$ with $xyz=1$.

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