# Tojamaru

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# 610 Questions

 27 To show that the set point distant by 1 of a compact set has Lebesgue measure $0$ 16 There exist an infinite subset $S\subseteq\mathbb{R}^3$ such that any three vectors in $S$ are linearly independent. 13 Subset of $\mathbb{Q}$ 12 Relation between area of a triangle on a sphere and plane 11 I need to calculate $x^{50}$ [duplicate]

# 10,731 Reputation

 +45 What is $(g \circ f)(3)$? +10 what will be the angle at the centre? +45 why is this true? $\lim_{x\to 0}\frac{\sin^2(x)}{x^2} = \lim_{x\to 0}\frac{\sin(x)}{x}$ +10 Suppose f is differentiable on an interval I. Prove that f' is bounded on I if and only if exists a constant M such that $|f(x) - f(y)| \le M|x - y|$

 26 Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$ 9 If $2^x=3^y=6^{-z}$ then prove that:$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0$ 7 $AB-BA=I$ having no solutions 7 Is $e^x$ the only isomorphism between the groups $(\mathbb{R},+)$ and $(\mathbb{R}_{> 0},*)$? 6 Basic group theory exercise

# 134 Tags

 81 real-analysis × 185 30 integration × 10 62 homework × 35 26 indefinite-integral × 2 59 calculus × 33 25 linear-algebra × 109 50 general-topology × 118 25 group-theory × 44 46 complex-analysis × 150 23 continuity × 30

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