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9856565651
@9856565651
July 2022
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Помогите решить 3 и 5
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oganesbagoyan
Verified answer
3)
f(x) =(4x-7)/(x² +4) , x(0) =0.
f '(x) =
(
(4x-7)/(x² +4)
)
' =
(
(4x-7)' *(x²+4) -(4x-7)*(x²+4)'
)/
(x² +4)² =
(
4(x²+4) -(4x-7)*2x
)/
(x² +4)² =(-4x² +14x +16)/(x²+4)².
f '(x(0))
=f '(0)
= (-4*0² +14*0 +16)/(0² +4)² =16/16
=1
.
************************************
5)
f(x) =3sinx+2 ,x(0) =π/3.
f '(x) =(3sinx+2)' = (3sinx)' +2' =3*(sinx)' +0 =3*cosx.
f '(x(0)) =
f '(π/3)
=3*cosπ/3 =3*1/2 =
1,5.
1 votes
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Answers & Comments
Verified answer
3) f(x) =(4x-7)/(x² +4) , x(0) =0.f '(x) =((4x-7)/(x² +4) ) ' =((4x-7)' *(x²+4) -(4x-7)*(x²+4)' )/(x² +4)² =
(4(x²+4) -(4x-7)*2x )/(x² +4)² =(-4x² +14x +16)/(x²+4)².
f '(x(0)) =f '(0) = (-4*0² +14*0 +16)/(0² +4)² =16/16 =1.
************************************
5) f(x) =3sinx+2 ,x(0) =π/3.
f '(x) =(3sinx+2)' = (3sinx)' +2' =3*(sinx)' +0 =3*cosx.
f '(x(0)) =f '(π/3) =3*cosπ/3 =3*1/2 =1,5.