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1

Qui vi mostriamo un esempio di soluzione passo-passo di limiti. Questa soluzione è stata generata automaticamente dalla nostra calcolatrice intelligente:

$\lim_{x\to\:5}\left(\frac{x^2-25}{x-5}\right)$

Simplify $\sqrt{x^2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $\frac{1}{2}$

$\frac{\left(x+\sqrt{25}\right)\left(\sqrt{x^2}-\sqrt{25}\right)}{x-5}$

Applicare la formula: $a^b$$=a^b$, dove $a=25$, $b=\frac{1}{2}$ e $a^b=\sqrt{25}$

$\frac{\left(x+5\right)\left(\sqrt{x^2}-\sqrt{25}\right)}{x-5}$

Simplify $\sqrt{x^2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $\frac{1}{2}$

$\frac{\left(x+5\right)\left(x-\sqrt{25}\right)}{x-5}$

Applicare la formula: $a^b$$=a^b$, dove $a=25$, $b=\frac{1}{2}$ e $a^b=\sqrt{25}$

$\frac{\left(x+5\right)\left(x- 5\right)}{x-5}$

Applicare la formula: $ab$$=ab$, dove $ab=- 5$, $a=-1$ e $b=5$

$\frac{\left(x+5\right)\left(x-5\right)}{x-5}$
2

Fattorizzazione della differenza di quadrati $x^2-25$ come prodotto di due binomi coniugati

$\frac{\left(x+5\right)\left(x-5\right)}{x-5}$
3

Applicare la formula: $\frac{a}{a}$$=1$, dove $a=x-5$ e $a/a=\frac{\left(x+5\right)\left(x-5\right)}{x-5}$

$x+5$
4

Valutare il limite $\lim_{x\to5}\left(x+5\right)$ sostituendo tutte le occorrenze di $x$ con $5$

$5+5$
5

Applicare la formula: $a+b$$=a+b$, dove $a=5$, $b=5$ e $a+b=5+5$

$10$

Final answer to the exercise

$10$

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