• Authenticity Guarantee

We guarantee authenticity

• Privacy Guarantee

• Plagiarism FREE

Writing that are 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

(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)

Word count difference + 1st-time order
with code: bestorder15
We have a GREAT 25%OFF
Get a Price Quote:
Total price:

(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