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terletskiyalex
@terletskiyalex
October 2021
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sangers1959
Verified answer
3.
y=3*cos³(3x)
y`=-27*sin(3x)*cos²(3x)
y``=-81*cos³(3x)+162*sin²(3x)*cos(3x)=
=3(54*sin²(3x)-27*cos³(3x)).
4.
lim(x→0) (e^x-e^(-x))/x=lim(x→0) (e^x-e^(-x))`/x`=
=(e^x-(-e^x)/1=2*e^⁰=2.
5.
y`=(-x⁴/4-2x³/3-3x²/2+2)`=0
-x³-2x²-3x=0 I×(-1)
x(x²+2x+3)=0 ⇒
x=0
y(-2)=-x⁴/4-2x³/3-3x²/2+2=-(-2)⁴-2*(-2)³/3-3*(-2)²/2+2=
=-16+16/3-12/2+2=-16+5¹/₃-6+2=-14²/₃
y(0)=-0-0-0+2=2=ymax
y(4)=-256+128/3-48/2+2=-256+42²/₃-24+2=-235¹/₃=ymin
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Answers & Comments
Verified answer
3.y=3*cos³(3x)
y`=-27*sin(3x)*cos²(3x)
y``=-81*cos³(3x)+162*sin²(3x)*cos(3x)=
=3(54*sin²(3x)-27*cos³(3x)).
4.
lim(x→0) (e^x-e^(-x))/x=lim(x→0) (e^x-e^(-x))`/x`=
=(e^x-(-e^x)/1=2*e^⁰=2.
5.
y`=(-x⁴/4-2x³/3-3x²/2+2)`=0
-x³-2x²-3x=0 I×(-1)
x(x²+2x+3)=0 ⇒
x=0
y(-2)=-x⁴/4-2x³/3-3x²/2+2=-(-2)⁴-2*(-2)³/3-3*(-2)²/2+2=
=-16+16/3-12/2+2=-16+5¹/₃-6+2=-14²/₃
y(0)=-0-0-0+2=2=ymax
y(4)=-256+128/3-48/2+2=-256+42²/₃-24+2=-235¹/₃=ymin