chwala's latest activity

I meant for uniform convergence, this must hold ##\lim _{n→∞} sup |f_n (x) - f(x) | =0## and in our case, ##\lim _{n→∞} sup |f_n (x)...

Thanks @WWGD , getting analysis slowly, in any case analysis is not that difficult as i had earlier thought, ... For uniform convergence...

Notice the limit function is discontinuous, which shows convergence isn't uniform. The limit of a sequence ##f_n \rightarrow f##...

Consider also ##e^{-n\sin \theta}## for ##\theta \in [0, \pi]##.

You should try to prove the non-uniformness of the two examples @WWGD and I gave to see that you cannot choose N independently of the...

clearer now, For ##f(x)=x^n ## on ##[0,1]## three cases to consider. Case 1 consider ##0 ≤x <1## ##x^n → 0, ∀ 0 ≤x <1 ## further...

Note that ##\sin(\frac{n\pi}{2}) = 0## if ##n## is even and alternates between ##\pm1## if ##n## is odd. Using the alternating series...

Clearly, the equation ## 4x^5u''+12x^2u'-4u=0 ## is not a Cauchy–Euler equation, and it cannot be solved by the standard method, which...

Doing some reading ... I want to analyse my problem further by firstly looking at existence and uniqueness. Re-writing it as a first...

ok man, I read that. The only thing remaining is for me to get to learn some analysis on this type of problem...

I’ve been exploring the limits of Cauchy–Euler type methods and constructed the following equation: ##4x^5 u'' + 12x^2 u' - 4u = 0##...

Review integration by partial fractions for the integral involving y.

$$\ln 10 e^{y\ln 10 }dy = \frac{dx}{x}$$ $$e^{y\ln 10 } = \ln |x |+ C$$ $$y= \frac{\ln(\ln |x| + C)}{\ln 10}$$defined for $$|x|...

##10^y dy = \dfrac{dx}{x\ln 10}## ##\int 10^y dy = \int \dfrac{dx}{x\ln 10}## ... ##10^y = \ln x +C## ##10^y = \ln (ax)##...

The roots of the equation in part (i) are the same as the roots in part (ii). Since in both cases we have equations of the form ax^2 +...