# Ku saabsan ogaysiinta hawlaha laamaha0820

Qaybaha qalooca waxaa loo isticmaalaa qoraalo qeexitaan shaqeed oo leh kala duwanaansho kiis. Waxaan dabagal ku sameynaa su'aasha fudud ee ah in matalaadan sidoo kale la baabi'in karo oo howsha loo yareyn karo ogeysiis sameyn karta la'aantood. Tusaale ahaan, shaqada

$$f: \mathbb{R} \to \mathbb{R}, f(x) = \left\{\begin{matrix} 42, & \text{falls } x = 0 \\ x, & \text{sonst} \end{matrix}\right.$$

Waxaan tixgelinaynaa taxanaha $$(x_n)$$ wata $$x_n = \frac{1}{n}$$ . Taxanahan $$\lim_{ n \to \infty } x_n = \lim_{ n \to \infty } \frac{1}{n} = 0$$ . Intaa waxaa sii dheer, $$\lim_{ n \to \infty } f(x_n) = \lim_{ n \to \infty } \frac{1}{n} = 0 \neq 42 = f(0)$$ . Marka $$f$$ waa la joojiyaa barta $$x=0$$ yacni gebi ahaanba waa la joojiyaa.

Maaddaama wadarta iyo wax soo saarka shaqooyinka joogtada ahi ay yihiin kuwo isdaba joog ah sababo la xiriira silsiladaha silsiladda, mid ayaa abuuri kara oo keliya hawlo joogto ah (gaar ahaan marna $$f$$ ) iyadoo la kaashanayo afarta hawlgal ee xisaabinta aasaasiga ah.

Si kastaba ha noqotee, haddii aan u oggolaano shaqada calaamadaha joojinta, tusaale ahaan, waxaan si fudud u heli karnaa ogeysiis noocaas ah. Kadibna waa

$$f: \mathbb{R} \to \mathbb{R}, f(x) = sgn^2(x-42)+42.$$

Shaqada guud $$f$$ leh kala duwanaansho kiis ayaa lagu dabaqayaa

$$f,g,h,a: \mathbb{R} \to \mathbb{R}, f(x) = \begin{Bmatrix} g(x), & \text{falls } a(x) = 0 \\ h(x), & \text{falls } a(x) \neq 0 \end{Bmatrix} = sgn^2 \left(a(x)\right)\cdot h(x) + \left(1-sgn^2\left(a(x)\right)\right)\cdot g(x).$$

$$f$$ sidoo kale waa la soo bandhigi karaa iyada oo aan jirin haddii / kale qaababka xakamaynta leh: