Nov
24
comment Prove that $F(1) + F(3) + F(5) + … + F(2n-1) = F(2n)$
and you start with which $n$? For $n=1$ you get $0=f(1)=f(2)=?$
Nov
24
answered Prove that $F(1) + F(3) + F(5) + … + F(2n-1) = F(2n)$
Nov
24
comment Prove that $F(1) + F(3) + F(5) + … + F(2n-1) = F(2n)$
Why do you use two different notations for the numbers? Either $f(n)$ of $F(n)$. Then numbers are $0,1,1,2,3,5,\ldots$. So if $f(5)=5$ then $f(1)=1, f(3)=2$.
Nov
24
reviewed Edit Solving this trigonometric task
Nov
24
revised Solving this trigonometric task
Replaced photo of equation with actual LaTEX.
Nov
23
revised $x,y,z$ are positive real numbers and $x+y+z=1$ $\implies$ $\bigg(1+\dfrac 1x\bigg)\bigg(1+\dfrac 1y \bigg)\bigg(1+\dfrac 1z \bigg)\ge 64$?
typo
Nov
23
revised Prove $\text{rad}(I)/I$ is isomorphic to $\mathfrak{N}(R/I)$
latex
Nov
23
reviewed Approve Finding a limit for n tends to infinity
Nov
23
reviewed Approve Determine if $\displaystyle \int_3^{\infty}\frac{x+1}{\sqrt{x^4-x}}\,dx $ converges
Nov
21
comment $P(x+2)=2x^3-4x^2+2x+3$. Find the remainder of $\dfrac{P(x)}{(x-3)}$
What does $P(u)=2(x-2)^3-4(x-2)^2+2(x-2)+3$ mean? Do you want the remainder of $P(x)/x-3=\frac{P(x)}{x}-3$ or of $P(x)/(x-3)=\frac{P(x)}{x-3}$
Nov
19
comment What is indefinite integral actually - $\int f(x)dx$ or $\int_a^x f(t)dt$?
How is a function $F(x)=\int_0^xf(t)dt$ connected with the antiderivates? It is an antiderivate of $f$ if $f$ is continous, so $F'(x)=(\int_0^xf(t)dt)'=f(x)$. To see this one has to proof that $\lim_{h \to 0} \frac{F(x+h)-F(x)}{h}=\lim_{h \to 0} \frac{\int_0^{x+h}f(t)dt-\int_0^xf(t)dt}{h}=\lim_{h \to 0} \frac{\int_x^{x+h}f(t)dt}{h}$ is equal to $f(x)$
Nov
19
comment What is indefinite integral actually - $\int f(x)dx$ or $\int_a^x f(t)dt$?
For example select $a=0$ and $f(t)=t^2$ and therefore $F(x)=\int_0^x t^2 dt$. So for $x=3$ the function value $F(3)$ is the definite integral $\int_0^3 t^2 dt$, which is $9$, for $x=4$ the function value $F(4)$ is the definite integral $\int_0^4 t^2 dt$, which is $64/3$
Nov
19
reviewed Approve What is indefinite integral actually - $\int f(x)dx$ or $\int_a^x f(t)dt$?
Nov
19
revised Arrange in increasing order of asymptotic complexity
latex, removed png
Nov
19
revised What is indefinite integral actually - $\int f(x)dx$ or $\int_a^x f(t)dt$?
added 40 characters in body
Nov
19
reviewed Reject A basic question on equilibrium point of coupled differential equation
Nov
19
reviewed Reject and Edit Functions and its powers
Nov
19
revised Functions and its powers
a pair of parantheses where missing
Nov
19
revised What is indefinite integral actually - $\int f(x)dx$ or $\int_a^x f(t)dt$?
added 108 characters in body
Nov
19
comment What is indefinite integral actually - $\int f(x)dx$ or $\int_a^x f(t)dt$?
you are right, thank you