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dogerti
@dogerti
November 2021
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помогите решить предел[tex] \lim_{x \to0} \frac{ \sqrt{x+9}-3}{sin3x} [/tex]
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sangers1959
Verified answer
Lim(x→0)(√(x+9)-3)/sin(3x))
Продифференцируем одновременно числитель и знаменатель:
lim(x→0) (1/(2*√(x+9))/(3*(cos(3x))=(1/(2*√0+9))/(3*cos(3*0))=
=1/(2*3)/(3*1)=(1/6)/3=1/18.
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Answers & Comments
Verified answer
Lim(x→0)(√(x+9)-3)/sin(3x))Продифференцируем одновременно числитель и знаменатель:
lim(x→0) (1/(2*√(x+9))/(3*(cos(3x))=(1/(2*√0+9))/(3*cos(3*0))=
=1/(2*3)/(3*1)=(1/6)/3=1/18.