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Must Waste More Time...
y = 8 - 0,5x² , x=1.
Уравнения касательной функции y = 8 - 0,5x² в точке с абсциссой xo= -2.
y -yo = y '(xo)*(x-xo); || yo =y(xo)_значения функции в точке xo = -2||
yo =8 -0,5(-2)² =8 -2 =6 ;
y ' =( 8 -0,5x²) ' = -x ⇒ y'(xo)= y ' | x=xo = -(-2) =2.
y -6 =2(x -(-2))⇔ y =2x +10.
1 1
S = ∫ (2x+10 -(8 -0,5x²)dx = ∫ (0,5x²+2x+2)dx =
-2 -2
(x³/6 +x² +2x) | a =-2 , b= 1 =1³/6 +1³+2*1 -( (-2)³/6 +(-2)² +2*(-2) ) =
= 4,5
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Must Waste More Time...
y = 8 - 0,5x² , x=1.
Уравнения касательной функции y = 8 - 0,5x² в точке с абсциссой xo= -2.
y -yo = y '(xo)*(x-xo); || yo =y(xo)_значения функции в точке xo = -2||
yo =8 -0,5(-2)² =8 -2 =6 ;
y ' =( 8 -0,5x²) ' = -x ⇒ y'(xo)= y ' | x=xo = -(-2) =2.
y -6 =2(x -(-2))⇔ y =2x +10.
1 1
S = ∫ (2x+10 -(8 -0,5x²)dx = ∫ (0,5x²+2x+2)dx =
-2 -2
(x³/6 +x² +2x) | a =-2 , b= 1 =1³/6 +1³+2*1 -( (-2)³/6 +(-2)² +2*(-2) ) =
= 4,5