Fiind the integral. integral 4(2x+5)^3 dx 3/4 (2x+5)^4 + C 1/4(2x+5)^4 + C 3/8(2
ID: 2878450 • Letter: F
Question
Fiind the integral. integral 4(2x+5)^3 dx 3/4 (2x+5)^4 + C 1/4(2x+5)^4 + C 3/8(2x+5)^4 + C 1/2 (2x+5)^4 + C integral e^xdx/e^x+e x/e + C e ln|e^x+e|+C x+C ln|e^x+e|+C Find values of x and y such that both f_x(x, y) = 0 and f_ytx, y) = 0. f(x, y) = x^3 - 4xy + 8y x = 2, y = 2 x = 4/3, y=2 x=2, y=3 x=0, y=0 Find the derivative of the function. f(x) = (x^2 - 2x + 2)(4x^3 - x^2 + 5) f(x) = 4x^4 - 32x^3 +30x^2 + 6x - 10 f(x) = 4x^4 - 36x^3 +30x^2 + 6x - 10 f(x) = 20x^4 - 32x^3 + 30x^2 + 6x - 10 f(x) = 20x^4 - 36x^3 + 30x^2 + 6x - 10 Find the area of the shaded region. 23/3 26/3 22/3 25/3 Evaluate the required second order partial derivative. Find f_yx(-4, -1) if f(x, y) = -2x^3y^2 - 3x^4 - 4xy^3. -396 -400 180 -384 Find the coordinates of the points of inflection for the function. f(x) = -x^2 - 14x - 48 (-7, 1) (-6, 0) (-8, 0) There are no points of inflection.Explanation / Answer
19)4(2x+5)3dx
substitute 2x+5=u
differentiate =>2dx +0=du => dx =(1/2) du
4(2x+5)3dx
=4u3(1/2) du
=2u3 du
=2(1/4)u4+C
=(1/2)u4+C
=(1/2)(2x+5)4+C
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20)exdx/(ex+e)
=ln|ex+e| +C
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21)f(x,y)=x3-4xy+8y
fx=3x2-4y , fy=-4x+8
fx=0 , fy=0
3x2-4y=0 , -4x+8=0
3x2-4y=0 , x=8/4
3x2-4y=0, x=2
3*22-4y=0
12-4y =0
4y=12
y =3
x=2, y =3
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22)f '(x)=20 x4 - 36 x3 + 30 x2 + 6 x - 10
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23) area =[0 to 2] (x2+3) dx=26/3
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24)f(x,y)=-2x3y2-3x4-4xy3
fy(x,y)=-4x3y-0-12xy2
fy(x,y)=-4x3y-12xy2
fyx(x,y)=-12x2y-12y2
fyx(-4,-1)=-12(-4)2(-1)-12(-1)2
fyx(-4,-1)=192-12
fyx(-4,-1)=180
--------------------------------
25)f(x)=-x2-14x-48
f '(x)=-2x-14-0
f "(x)=-2
no inflection point
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