Помогите пожалуйста решить с объяснением lim(x→0) ⁡(1 – √(1 – x^2 ))/x^2. Created by mariyatimoshenko. algebra-ru

x^2...

mariyatimoshenko @mariyatimoshenko

September 2021 1 12 Report

Помогите пожалуйста решить с объяснением
lim(x→0) ⁡(1 – √(1 – x^2 ))/x^2

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oganesbagoyan

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task/26015259
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lim(x→0) ⁡(1 – √(1 – x^2 ))/x^2
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неопределенность типа 0/0
lim ⁡(1 – √(1 – x² ))/ x² = lim ⁡(1 – √(1 – x² )) *(1 + √(1 – x²) )/ x² =
x→0 x→0
lim ⁡(1 – √(1 – x² )) *(1 + √(1 – x²) )/ x²(1 + √(1 – x²) ) =
x→0
lim ⁡(1² – (1 – x² )) / x²(1 + √(1 – x²) ) =lim ⁡1/ (1 + √(1 – x²) ) =
x→0 x→0
=1/(1+√((1 – 0²) ) =1/2 .

ответ : 1/2 .
* * * * * * * * * *
* * * (a+b)(a-b) =a² - b² . (√(1 -x²) ) =1-x² ; (√A)² =A A ≥0 * * *

2 votes Thanks 1

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