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Writing that is plagiarism free # Free Math Essay Sample

. Differentiate with respect to x

(a)

F(x) =   1/3 x7

F(x) = 1/3x -7

FI(x) = -7/3x-8

fI(x)= -7/3x8

Get a Price Quote:

(b)

If f(x) =  g(x)/h(x)

fI(x)= (h(x) gI(x) - g(x)hI(x))/h(x)2

=(x-5) (12x2-4x3) / (x-5)2

= (12x3-60x2-4x3)/ (x2-10x+25)

= (  8x3-60x2) /(x2-10x+25)

(c)

F(x) = (2x2-6)3(3x3-3)

F(x) = g(x)h(x)

fI(x)= g(x) hI(x) + h(x)gI(x)

fI(x) = (2x2-6)2(3x3-3)I+((2x2-6)3)I(3x3-3)

= (2x2-6)2(2x2-6)27x2+((2x2-6)3)I(3x3-3)

=((2x2-6)3)I=U3=3U2=3(2x2-6)2(4x)

= (2x2-6)2(2x2-6)27x2+12x (2x2-6)(3x3-3)

=(4x4-24x2+36)(2x2-6)27x2+12x (4x4-24x2+36)(3x2-3)

=(4x4-24x2+36)(54x4-162x2)+ (48x5-288x3+432x)(3x2-3)

=216x8-1296x8+1944x4-648x8+3888-5832x2 +144x7+864x5+1296x3-144x7+864x5-1296x

fI(x)=-1728x8+1720x5+1944x4+1296x3-5832x2-1296x+3888

(d)

F(x) = xln(2x)

We know dlnU/dx=UI/U

Also F(x)=g(x)h(x)

fI(x)=g(x)hI(x)+h(x)gI(x)

= 2x/2x+ln (2x)

TR=P x Q,                           TR- Total Revenue

TR = 400Q - Q2/50

Expression for marginal revenue is,

MR = 400 - Q/25

MR = 400 - 10000 / 25

MR=0

Price elasticity demand when price=100

P = 400 - Q/50

Q/50 = 400 - P

Q=400 x 50 - 50P,

=-50 x 100/10000

=-1/3 hence inelastic

c) Henry can maximize daily revenue by either increasing the quantity of the commodities. Increase in price may not affect demand for the commodity due to the inelastic demand for the commodity. Increasing the quantity is the only way to maximize profit hence revenue.

a)     A=P(1+R)n

A=P(1+24/1200)12

A=P(1+0.02)12

=P(1.02)12

=1.2682P

I=PRT

R=I/PT = 0.2682P / P=0.2682

=26.82%

b) A=P(1+R)n

A=P(1+R/4)4n

A= P(1+6/400)24

A=12000(1.015)24

A=1.4295 x 12000

=\$17154.03

C) 5/100x 1000x 40 = £ 2000

4. Express the first and the second order derivatives of;

(a)

fI(x,y) = 12x + 5 dy/dx

fII(x,y) = 12 + d2y/dx2

(b) f(x,y) = 3x5y4

fI(x,y)= 15x4y4+3x54y3dy/dx

fII(x,y)= 60x3y4+15x44y3dy/dx+15x4y3dy/dx+3x512y2d2y/dx2

c) f(x,y)=(10+x2y)3

fI(x,y)=U3=3U2.UI

=3(10+x2y)2 (2xy+ x2dy/dx)

Using f(x) =h(x)g(x)

fI(x,y)= h(x)gI(x)+hI(x)g(x),

fI(x,y) = (10+x2y)2(2y+ 2xdy/dx+2xd2y/dx2)+(2xy+x2dy/dx)

fI(x,y)=(300+60x2y+3x4y2)(2xy+x2dy/dx)

=(600xy+120x3y2+6x5y3+300x2dy/dx+60x4ydy/dx+3x6y2dy/dx)

fII(x,y)=600y+600xdy/dx+360x2y2+120x32ydy/dx+30x4y3+6x53y2dy/dx+600xdy/dx+240x3…ydy/dx+60x4d2y/dx2+18x5y2dy/dx+3x62yd2y/dx2.   Have NO Inspiration