List questions from radicals

Published on 21 Jan 2017 - 4:59

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Evaluate $\lim _{x\to \infty }\left(\cos\sqrt{x}-\cos\sqrt{x-1}\right)$

Published on 01 Apr 2026 - 4:20

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Taking square roots in inequalities

Published on 21 Jan 2017 - 12:23

80

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How to show $f(x) =(\sqrt[3]{x}+x)\sqrt{x}$ is injective and surjective?

Published on 22 Jan 2017 - 18:23

143

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Exponent Laws and Square Roots of Squares

Published on 22 Jan 2017 - 20:52

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reverse of $f(x) = 1 + \tan(x^2)$

Published on 28 Mar 2026 - 11:13

66

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Solve the inequality $\sqrt{4x+1}+\sqrt{x+1}<x+1$

Published on 24 Jan 2017 - 18:58

190

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How to solve a system of 3 trigonometric equations

Published on 24 Jan 2017 - 19:40

335

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Limit $\lim_{n\to\infty} n^{-3/2}(1+\sqrt{2}+\ldots+\sqrt{n})=\lim_{n \to \infty} \frac{\sqrt{1} + \sqrt{2} + ... + \sqrt{n}}{n\sqrt{n}}$

Published on 25 Jan 2017 - 21:43

126

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Weird limit: $\lim_{n\to\infty}\left(\frac{f(1)+f(2)+...+f(n)}{n}\right)^n$

Published on 30 Mar 2026 - 8:36

541

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Given that $ab + c^2 = 18$ and $a^2 + b^2 = 12$, Find $abc$

Published on 27 Jan 2017 - 12:56

315

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Prove that $\ln{n} \lt \sqrt{n}$ for $n \in \mathbb{N}^{*}$ without derivative

Published on 27 Jan 2017 - 13:06

95

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Trigonometric system of 3 modular equations

Published on 25 Mar 2026 - 7:42

130

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Solve for x (quadratic equation)

Published on 29 Mar 2026 - 4:49

76

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How to intuitively deduce the relationship among exponent, log and root?

Published on 29 Jan 2017 - 6:42

List Question

simplify $4\sqrt{3-2x^2}-1$

Evaluate $\lim _{x\to \infty }\left(\cos\sqrt{x}-\cos\sqrt{x-1}\right)$

Taking square roots in inequalities

How to show $f(x) =(\sqrt[3]{x}+x)\sqrt{x}$ is injective and surjective?

Exponent Laws and Square Roots of Squares

reverse of $f(x) = 1 + \tan(x^2)$

Solve the inequality $\sqrt{4x+1}+\sqrt{x+1}<x+1$

How to solve a system of 3 trigonometric equations

Limit $\lim_{n\to\infty} n^{-3/2}(1+\sqrt{2}+\ldots+\sqrt{n})=\lim_{n \to \infty} \frac{\sqrt{1} + \sqrt{2} + ... + \sqrt{n}}{n\sqrt{n}}$

Weird limit: $\lim_{n\to\infty}\left(\frac{f(1)+f(2)+...+f(n)}{n}\right)^n$

Given that $ab + c^2 = 18$ and $a^2 + b^2 = 12$, Find $abc$

Prove that $\ln{n} \lt \sqrt{n}$ for $n \in \mathbb{N}^{*}$ without derivative

Trigonometric system of 3 modular equations

Solve for x (quadratic equation)

How to intuitively deduce the relationship among exponent, log and root?

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