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XeniyaTyan
@XeniyaTyan
December 2021
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найдите значение предела функции
x^4-27x+x^3-27/3x-9
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ShirokovP
Verified answer
Lim x->3 (
x^4 - 27x + x^3 - 27)/(3x - 9) = [ 0/0]
lim x->3 (x(x^3 - 27) + 1(x^3 - 27))/3 (x - 3) =
= lim x->3 ((x^3 - 27)(x + 1))/ (3 (x - 3)) =
= lim x->3 ((x - 3)(x^2 + 3x + 9)(x + 1))/ (3 (x - 3)) =
= lim x->3 ((x^2 + 3x + 9)(x + 1))/ 3 =
= ((3^2 + 3*3 + 9)(3 + 1))/3 =
= 108/3 = 36
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Answers & Comments
Verified answer
Lim x->3 (x^4 - 27x + x^3 - 27)/(3x - 9) = [ 0/0]lim x->3 (x(x^3 - 27) + 1(x^3 - 27))/3 (x - 3) =
= lim x->3 ((x^3 - 27)(x + 1))/ (3 (x - 3)) =
= lim x->3 ((x - 3)(x^2 + 3x + 9)(x + 1))/ (3 (x - 3)) =
= lim x->3 ((x^2 + 3x + 9)(x + 1))/ 3 =
= ((3^2 + 3*3 + 9)(3 + 1))/3 =
= 108/3 = 36