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barcode in ssrs 2008 Copyright 2008, 1997, 1985 by The McGrawHill Companies, Inc. Click here for terms of use. in Visual Studio .NET
Copyright 2008, 1997, 1985 by The McGrawHill Companies, Inc. Click here for terms of use. QRCode Reader In VS .NET Using Barcode Control SDK for .NET Control to generate, create, read, scan barcode image in VS .NET applications. QR Generation In VS .NET Using Barcode encoder for VS .NET Control to generate, create QR Code image in VS .NET applications. CHAP. 19] Scan QR Code In Visual Studio .NET Using Barcode decoder for VS .NET Control to read, scan read, scan image in VS .NET applications. Bar Code Generator In .NET Framework Using Barcode generation for VS .NET Control to generate, create barcode image in VS .NET applications. INSTANTANEOUS RATE OF CHANGE
Recognizing Barcode In Visual Studio .NET Using Barcode reader for .NET Control to read, scan read, scan image in .NET applications. QR Code Generation In C# Using Barcode creator for .NET framework Control to generate, create QRCode image in .NET framework applications. If and
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Print UPC  13 In None Using Barcode creation for Font Control to generate, create EAN13 image in Font applications. Barcode Maker In .NET Framework Using Barcode creator for Reporting Service Control to generate, create barcode image in Reporting Service applications. x is 2.01, and the new volume is (2.01)3 = 8.120 601. So, 0.120 601 y = = 12.0601 x 0.01
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Universal Product Code Version A Creator In None Using Barcode drawer for Word Control to generate, create UPCA image in Microsoft Word applications. Make Code 39 Extended In VS .NET Using Barcode printer for Reporting Service Control to generate, create Code 3/9 image in Reporting Service applications. Let us extend the result of the above example from y = x 3 to an arbitrary differentiable function y = f (x). Consider a small change x in the value of the argument x. The new value of the argument is then x + x, and the new value of y will be f (x + x). Hence, the change y in the value of the function is y = f (x + x) f (x) EAN13 Decoder In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. Barcode Decoder In .NET Using Barcode decoder for Visual Studio .NET Control to read, scan read, scan image in .NET framework applications. The ratio of the change in the function value to the change in the argument is y f (x + = x x) f (x) x The instantaneous rate of change of y with respect to x is de ned to be lim y f (x + = lim x 0 x x) f (x) = f (x) x x close to 0, y/ x will be close The instantaneous rate of change is evaluated by the derivative. It follows that, for to f (x), so that y f (x) x (19.1) Solved Problems
19.1 The weekly pro t P, in dollars, of a corporation is determined by the number x of radios produced per week, according to the formula P = 75x 0.03x 2 15 000 (a) Find the rate at which the pro t is changing when the production level x is 1000 radios per week, (b) Find the change in weekly pro t when the production level x is increased to 1001 radios per week. (a) The rate of change of the pro t P with respect to the production level x is dP/dx = 75 0.06x. When x = 1000, dP = 75 0.06(1000) = 75 60 = 15 dollars per radio dx INSTANTANEOUS RATE OF CHANGE
[CHAP. 19
(b) In economics, the rate of change of pro t with respect to the production level is called the marginal pro t. According to formula (19.1), the marginal pro t is an approximate measure of how much the pro t will change when the production level is increased by one unit. In the present case, we have P(1000) = 75(1000) 0.03(1000)2 15 000 = 75 000 30 000 15 000 = 30 000 P(1001) = 75(1001) 0.03(1001)2 15 000 = 75 075 30 060.03 15 000 = 30 014.97 P = P(1001) P(1000) = 14.97 dollars per radio which is very closely approximated by the marginal pro t, 15 dollars, as computed in part (a). 19.2 The volume V of a sphere of radius r is given by the formula V = 4 r 3 /3. (a) How fast is the volume changing relative to the radius when the radius is 10 millimeters (b) What is the change in volume when the radius changes from 10 to 10.1 millimeters dV 4 3 = Dr r dr 3 When r = 10, dV = 4 (10)2 = 400 400(3.14) = 1256 dr (b) 4 4000 (10)3 = 3 3 4 4121.204 4 V (10.1) = (10.1)3 = (1030.301) = 3 3 3 V (10) = V = V (10.1) V (10) = 4121.240 4000 3 3 3.14 = (4121.204 4000) = (121.204) (121.204) 3 3 3 = 126.86 cubic millimeters The change predicted from (19.1) and part (a) is V dV dr r = 1256(0.1) = 125.6 cubic millimeters = 4 (3r 2 ) = 4 r 2 3 19.3 An oil tank is being lled. The oil volume V , in gallons, after t minutes is given by V = 1.5t 2 + 2t How fast is the volume increasing when there is 10 gallons of oil in the tank [Hint: To answer the question, how fast , you must always nd the derivative with respect to time.] When there are 10 gallons in the tank, 1.5t 2 + 2t = 10 Solving by the quadratic formula, t= 2 4 4(1.5)( 10) 2 4 + 60 2 64 2 8 = = = =2 2(1.5) 3 3 3 or 10 3 or 1.5t 2 + 2t 10 = 0 CHAP. 19]

