Materi : Limit Fungsi Kelas/Semester : 11/2 [tex]\lim_{a \to \ x} \frac{a^{n}-x^{n}}{a-x} [/tex]

Mapel Matematika
Bab Limit

Lim a^n - x^n / a - x
a ➡ x

= Lim. (a - x)(a^n-1 + xa^n-2 + ... + x^n-1) / (a - x)
a ➡ x

= Lim (a^n-1 + xa^n-2 + ... + x^n-1)
a ➡ x

= x^n-1 + x(x)^n-2 + ... + x^n-1
= x^n-1 + x^n-1 + ... + x^n-1
= nx^n-1

Limit aⁿ - xⁿ / a - x
a ➡️x
f (a) ke f (x) = xⁿ
f'(a) = limit f(a) - f(x) / a - x = aⁿ - xⁿ / a - x
a ➡️x

= Lim aⁿ - xⁿ / a - x = nxⁿ¯¹ ✔️
a ➡️x

Semoga bermanfaat.....
-Prisco