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Calculus for Engineering Students

In: Science

Submitted By verdant
Words 472
Pages 2
Question one
On the interval [2, 9] integrate:

∫ (3x²-4) dx = x³-4x = (729-36) - (8-8)
= 693+0 = 693

Average value over the interval is

693
Question two

Find the area of the shaded region. 2) f(x) = -x3 + x2 + 16x, g(x) = 4x
-x3 + x2 + 16x = 4x
-x3 + x2 + 16x-4x = 0
-x3 + x2 + 12x = 0 x(-x2+ x + 12) = 0 x=0 or x2-4x+3x-12 X(x-4)+3(x-4) = 0 x=0, x=-3,x=4
A = ∫ ((x2- x -12) dx = [x3/3- x2/2 -12x] + [x3/3- x2/2 - 12x]
A = [-9 + 4.5 + 36] + [64/3 – 8 – 48]
A = [31.5] + [-34.666]
A= 3.16666units sq
Question three
Find f(4, 3, 6) when f(x, y, z) = 4x2 + 4y2 - z2.
We substitute x, y and z with 4, 3 and 6
F(x,y,z)=4x2+ 4y2+ z2 =4(4)2+ 4(3)2+ (6)2 =4(16) + 4(9) +36 = 64 + 36 +36 = 136

Question four
Suppose the supply and demand functions of a certain item are given by S (q) = 4q + 2 D (q) = 14 - q2. Find the requested information. (3 pts.) a) Equilibrium Point Equilibrium point is where quantity demanded = supply supplied 14 - q2 = 4q + 2 - q2 -4q +12=0 q2 + 4q -12=0 q2 +6q-2q -12=0 q(q+6) -2(q+6) =0
(q-2)(q+6)= 0
Q=2 or q = -6
The equilibrium point is where q = 2.
Get me your contacts so that next time we can talk. Please send it inform of a document. Thanks b) Producer Surplus 14 - q2 > 4q + 2 - q2 -4q +12>0 q2 + 4q -12>0 q2 +6q-2q -12>0 q(q+6) -2(q+6) >0 (q-2)(q+6)> 0 q=2 or q = -6
Produder surplus is at point above 2 c) Consumer Surplus 14 - q2 > 4q + 2 - q2 -4q +12>0 q2 + 4q -12>0 q2 +6q-2q -12>0 q(q+6) -2(q+6) >0 (q-2)(q+6)> 0 q>2 or q >-6
Produder surplus is at point above 2
14 - q2 < 4q + 2 - q2 -4q +12<0 q2 + 4q -12<0 q2 +6q-2q -12>0 q(q+6) -2(q+6) < 0 (q-2)(q+6)< 0 q<2…...

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