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(3) (i) A broken pipe at an oil

(3) (i) A broken pipe at an oil

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(3) (i) A broken pipe at an oil rig off the east coast of Trinidad produces a circular oil slick that is S meters thick at a distance x meters from the break. It difficult to measure the thickness of the slick directly at the source owing to excess turbulence, but for x>0 they know that x 5 -+-x 2 3 ²+x² +2x S(x) = If the oil slick is assumed to be continuously distributed, how thick is expected to be at the source? ( 4x+7 (iї) If f(x)- |4x² – 1 1<x<2 ,determine whether the function f(x) is continuous 2<x<4 throughout its domain?
Transcribed Image Text:(3) (i) A broken pipe at an oil rig off the east coast of Trinidad produces a circular oil slick that is S meters thick at a distance x meters from the break. It difficult to measure the thickness of the slick directly at the source owing to excess turbulence, but for x>0 they know that x 5 -+-x 2 3 ²+x² +2x S(x) = If the oil slick is assumed to be continuously distributed, how thick is expected to be at the source? ( 4x+7 (iї) If f(x)- |4x² – 1 1<x<2 ,determine whether the function f(x) is continuous 2<x<4 throughout its domain?
(1) If the total cost of a firm is C(x)=1.5x – 5x² +20x+5. Find the marginal cost (in dollars) when 25 units are produced and sold. (2) The number q of roller blades a firm is willing to sell per week at a price of Sp is given by q = 60 p+25 +300 for 20<ps100. dq (i) Find dp (ii) Find the amount supplied when the price is $56. (ii) Find the instantaneous rate of change of supply with respect to price when the price is $56.
Transcribed Image Text:(1) If the total cost of a firm is C(x)=1.5x – 5x² +20x+5. Find the marginal cost (in dollars) when 25 units are produced and sold. (2) The number q of roller blades a firm is willing to sell per week at a price of Sp is given by q = 60 p+25 +300 for 20<ps100. dq (i) Find dp (ii) Find the amount supplied when the price is $56. (ii) Find the instantaneous rate of change of supply with respect to price when the price is $56.
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