Summation of e^x and proof that the derivative of e^x=e^x Hard Problem: The expression ex can be written asex=n=0xnn!Where n! = n(n − 1)(n − 2) ... (2)(1). Show thatdex = exdxHint: Write out the first few terms of the summation. Recall that 0!=1.

To solve this problem, we need to show that the derivative of ( ex ) with respect to ( x ) equals (…

Answered: Hard Problem: The expression ex can be…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Differentiate the following function: y = (10x – 3)? O Y'= 20( x - 3) O Y'= 20(10x+3) O Y'= 20(10x-3) O Y'= 2 (10x-3)
Whenever postage rates change, some newspaper publishes a graph such as the one shown below, which shows the price of a first-class stamp from 2006 to 2016. Cost(dollam) 0.85- 0.70- 0.55 0.40 0.25 of 2006 2008 Price of a First-Class Stamp [Select] 2010 Year 2012 2014 2016 (a) Let f be the function whose rule is f(x) = cost of a first-class stamp in year x. Find f(2012) and f(2015). f(2012) = [Select] f(2015): =
Cost of buying tomato plants are 20 cents each and a farmer sells them for 50 cents each. His fixed costs are euro 60 including the rate he pays to the local council. How many tomato plants must he sell to break even? What kind of profit will he realize from selling 180 plants? Formulate P(x) function clearly and graph it. Values of its intersections with both axes must be clear.
Technology B uses 4 workers and 2 tonnes of coal to produce 100 meters of cloth. The worker's wages cost $10 and coal costs $5. We have previously calculated that the total cost of production is $50 and that the vertical intercept of the isocost line is 10.If there was a technology that used 1 more worker, how much would it have to decrease the coal required in order to cost the same? (Note: this is the absolute value of the slope of the isocost line.)
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New ads have been proposed and cost the company $5000 to run in each time slot. If the extra sales from each new ad are determined be sales = 11000 - 30ad. How many ads should be run? (enter as an integer).
Find f'(x). T(x) = 2x° (x* - 2) 5 f'(x) =O
5. Consider the process where S0 = 0 and {ut : t ∈ Z} is an i.i.d. random variable with N(0,σ2). a) DeterminethemeanandcovariancefunctionoftheprocessSt.Isthisprocessstrictlystationary?Second-order stationary? b) Show that the process Yt = (1 − L)St , t = 1,2,... is strictly stationary. Compute its mean and autocovariance function.
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1. Prepare the scatter diagram and insert the trendline or line of best-fit. Use a scaleof 2 cm to represent 1,000 units on the x-axis & 2 cm to represent $50,000 on the y-axis. 2. Using the line of best-fit, determine the company’s fixed cost per month and thevariable cost per unit. (Use 0 & 5,000 units.)
Solve for x for the following equation: 4ln(3x-8) = 60
Anation with fixed quantities of resources is able to produce any of the following combinations of carpet and carpet looms: Yards of Carpet (Millions) Carpet Looms (Thousands) 75 60 20 45 35 30 45 15 50 50 These figures assume that a certain number of previously produced looms are available in the current period for producing carpet. To answer this question, assume carpet looms is on the y-axis and yards of carpet is on the x-ais The plot of these points that make up the PPF has a vertical intercept of and a horizontal intercept of This PPF would be (Enter your responses as a wvhole number) bowed out a straight line

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Hard Problem: The expression ex can be written as ex = n=0 xn n! Where n! = n(n − 1)(n − 2) ... (2)(1). Show that d ex = ex dx Hint: Write out the first few terms of the summation. Recall that 0!=1.