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Prove that following recursively defined sequence converges and its limit is 1/2

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#real-analysis #sequences-and-series #convergence-divergence #cauchy-sequences #monotone-functions
53
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$f$ is increasing on open balls then $f$ is increasing on throughout open interval

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#real-analysis #continuity #monotone-functions
970
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Any epsilon-delta proof of the continuity of the inverse of a real-valued strictly monotonic continuous function on an open interval?

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#calculus #real-analysis #continuity #inverse-function #monotone-functions
127
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stochastic dominance and monotone functions

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#probability #monotone-functions
47
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Monotonic path terminology

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#geometry #algorithms #tangent-line #monotone-functions #projection
3.9k
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How to show this sequence is decreasing

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#sequences-and-series #factorial #monotone-functions
673
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Should every injective function be non monotonic?

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#functions #monotone-functions
169
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Set the monotone interval of function $f(x)=x+\sqrt{x^2+2x}$

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#calculus #ordinary-differential-equations #limits #derivatives #monotone-functions
42
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Specify the monotonicity based on the functional equation $f\bigl(f(x)\bigr)=f(x)-\frac{x}{4}$

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#functional-equations #monotone-functions
70
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Given function $g$ continuous in line $[0,\infty)$...

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#calculus #real-analysis #limits #convergence-divergence #monotone-functions
69
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Non-Monotonicity of Function with Definition Changing w.r.t. Rational/Irrational Input

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#real-analysis #analysis #irrational-numbers #monotone-functions
48
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Product of monotonically-decreasing sequence $x_n$ diverges if $x_i>1$?

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#real-analysis #sequences-and-series #limits #infinite-product #monotone-functions
96
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Prove using calculus or otherwise the following inequality

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#calculus #algebra-precalculus #monotone-functions
352
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Strict monotonicity of the partial derivatives of a strictly convex function

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#derivatives #convex-analysis #partial-derivative #monotone-functions
66
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Nonmonotone functions

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#real-analysis #monotone-functions

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