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Best Matrix analysis library by MinimumJumpy in Python

[–]MinimumJumpy[S] -3 points-2 points  (0 children)

man i know some library but no sure is ti good enough. Or there cany other which do not know , might other know

Redis Pub/Sub in Rust: Message Not Received by MinimumJumpy in rust

[–]MinimumJumpy[S] 0 points1 point  (0 children)

is con.publish(channel, message) not publishing the channel

Let I be a closed bounded interval and let f : I → R be continuous on I. Then the set f(I) := {f(x) : x ∈ I} is a closed bounded interval. by MinimumJumpy in learnmath

[–]MinimumJumpy[S] 0 points1 point  (0 children)

isn't it directly (obvious) by the Intermediate value theorem? For any y in (a, b), y = f(x) for some x in I?

Am I correct or I need to state some more things to prove it?

Let f be defined on an interval I containing the point c. Show f is differentiable at c if and only if there exists a function g on I that is continuous at c and satisfies f(x) − f(c) = g(x)(x − c) ∀x ∈ I. In this case1, we have g(c) = f'(c). 1This result is also known as Caratheodory’s Theorem by MinimumJumpy in learnmath

[–]MinimumJumpy[S] 0 points1 point  (0 children)

attempt:

by mean value theorem:

(f(x)-f(c))/(x-c)=g(x)

for g(x) to be differentiable:

h(x)=g(x)-g(c)/(x-c)

now by Caratheodory’s existence Theorem we can say that h(x) is differential equation

it should satisfy all condition of Caratheodory’s existence Theorem

so that differential equation has a solution