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15
410
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Prove $\sqrt{n^2 + 1} - n$ is strictly decreasing

Published on
#calculus #monotone-functions
628
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Prove integral diverges

Published on
#calculus #improper-integrals
142
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Prove the existence of a solution to the system by using the Implicit Function Theorem

Published on
#calculus #real-analysis #implicit-function-theorem
36
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Show that a set admits a tangent plane

Published on
#calculus #real-analysis #derivatives
318
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Prove $2 \cdot \sum\limits_{k = 0}^{n} \binom{2n}{2k} = 2^{2n}$ without induction

Published on
#calculus #real-analysis #combinatorics #binomial-coefficients #binomial-theorem
110
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Product of convex functions with special properties

Published on
#calculus #analysis #limits #functions #convex-analysis
34
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Show that solutions to a system form a graph of a function

Published on
#calculus #real-analysis #derivatives #implicit-function-theorem
950
Views

Approximating the value of an integral to six decimal places using a power series

Published on
#calculus #summation
50
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Recursive sequence problem (while it oscillates)

Published on
#calculus #sequences-and-series #limits #convergence-divergence
571
Views

Solve limit with Riemann sum.

Published on
#calculus #limits
123
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Sequence $(\frac{a_n}{n})$ is convergent.

Published on
#real-analysis #calculus #sequences-and-series #limits #analysis
315
Views

Prove that $f'(x) = \lim_{h\to 0^+ \\k\to 0^+} \frac{f(x+h) - f(x-k)}{h+k}$

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#calculus #real-analysis #limits #epsilon-delta
47
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Showing $\Phi(a+\text{weight}\cdot b) \neq (1-\text{weight})\cdot\Phi(a)+\text{weight}\cdot \Phi(a+b)$ where $\Phi(\cdot)$ is the CDF of $N(0,1)$

Published on
#calculus #probability-distributions #normal-distribution
87
Views

How to find $x$ in $\sum\limits_{i=1}^{\infty}\sum\limits_{j=1}^{\infty}x^{ij}=\frac{1}{1-\gamma}$ if $0\lt x\lt1$?

Published on
#calculus #sequences-and-series #euler-mascheroni-constant
61
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An inequality with operator norm

Published on
#calculus #functional-analysis #inequality

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