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Calculus: Power Rule | A General Approach / Advanced Calculus / Problems On Calculus (2) (3) (4)
Question On CALCULUS Help Pls!! by ToksZee(f): 5:51pm On Jan 27, 2021 |
Pls help! dy/dx Y=3x²-7x-4 And dy /dx Y=7x Pls "Solve using first principle " |
Re: Question On CALCULUS Help Pls!! by ab11baddo(m): 6:24pm On Jan 27, 2021 |
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Re: Question On CALCULUS Help Pls!! by BLACKARABIAN: 8:32pm On Jan 27, 2021 |
ToksZee:Lim(as h tends To 0) (3(x+h)/\2-7(x+h)-4-3(x)/\2-7(x)-4)/h....simplify and Make Sure You Get Rid Of the h(denomator). Before Plugging 0. Do Same For The Second Question. Na java phone I De Use, i For Solve Am Upload. |
Re: Question On CALCULUS Help Pls!! by Martinez39s(m): 10:25pm On Jan 27, 2021 |
ToksZee:Δy = 3(x + Δx)2 – 7(x + Δx) – 4 – 3x2 + 7x + 4 = 6x(Δx) + 3(Δx)2 – 7Δx Δy/Δx = 6x + 3(Δx) – 7 The limit of 6x + 3Δx – 7 as Δx approaches 0 is 6x – 7. Hence dy/dx = 6x – 7. And dy /dxΔy = 7(x + Δx) – 7x = 7(Δx) Δy/Δx = 7. The limit of 7 as Δx approaches 0 is 7. Hence dy/dx = 7. 3 Likes 2 Shares |
Re: Question On CALCULUS Help Pls!! by Bodyodour: 11:45pm On Jan 27, 2021 |
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Re: Question On CALCULUS Help Pls!! by Lordsagna: 9:16am On Jan 28, 2021 |
Martinez39s: bro I take God beg you help me with this A utility company has a small power plant that can produce a kilowatt hours of electricity daily at a cost of 10 - (x/10^5 )cents each for 0 < x < 8 x 10^5. Consumers will use 10^5(10 - p/2) kilowatt hours of electricity daily at a price of p cents per kilowatt hour. What price should the utility charge to maximize its profit? |
Re: Question On CALCULUS Help Pls!! by Lordsagna: 9:24am On Jan 28, 2021 |
Lordsagna: someone should help pls |
Re: Question On CALCULUS Help Pls!! by Martinez39s(m): 3:13pm On Jan 28, 2021 |
Lordsagna:I don't understand your question. Restate it again. It seems like an optimisation problem in differential calculus. Also clarify if you meant 10 – (x/10⁵) instead of (10 – x)/10⁵. I will solve the problem for you. |
Re: Question On CALCULUS Help Pls!! by Lordsagna: 4:05pm On Jan 28, 2021 |
Martinez39s: yeah it's on optimization but I'm stuck. 10 -(x/10^5) |
Re: Question On CALCULUS Help Pls!! by joshajay(m): 4:07pm On Jan 28, 2021 |
See Attached files for solutions.
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Re: Question On CALCULUS Help Pls!! by Martinez39s(m): 4:21pm On Jan 28, 2021 |
Lordsagna:I have gotten that it's 10 – (x/10⁵). For one last time, check your question again. |
Re: Question On CALCULUS Help Pls!! by Lordsagna: 5:11pm On Jan 28, 2021 |
Martinez39s:nothing is wrong with the question bro 3-b
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Re: Question On CALCULUS Help Pls!! by Hamzasaid(m): 7:46pm On Jan 28, 2021 |
Lordsagna: Solving Optimization Problems 1.Understand the problem. Clearly identify what quantity is to be maximized or minimized.(in this case,we are looking for the price that will maximize the profit) 2.Create equations relevant to the context of the problem, using the information given. (One of these should describe the quantity to be optimized. We'll call this the fundamental equation. i.e P(x)=R(x)-C(x)=> P(x)=xS.P(x)-C.P(x),,,,,,,,,, s.p(selling price),c.p(cost price),P(profit). critical point is at P'(x)=0) 2.If the fundamental equation defines the quantity to be optimized as a function of more than one variable, reduce it to a single variable function using substitutions derived from the other equations. 3.Identify the domain of this function, keeping in mind the context of the problem. which is (0<x<8*10^5)=>[0, 8*10^5] 4.Find the extreme values of this function on the determined domain. 5.then finally Identify the values of all relevant quantities of the problem. my little contribution in helping you solving the problem |
Re: Question On CALCULUS Help Pls!! by Lordsagna: 10:01pm On Jan 28, 2021 |
Hamzasaid: I'm grateful sir. |
Re: Question On CALCULUS Help Pls!! by Hamzasaid(m): 11:02pm On Jan 28, 2021 |
Re: Question On CALCULUS Help Pls!! by Lordsagna: 8:49am On Jan 29, 2021 |
Hamzasaid:. yeah..I gat a large value not sure if it's right. |
Re: Question On CALCULUS Help Pls!! by Timoken: 9:31am On Jan 29, 2021 |
Solution. y=3x² -7x-4 Change in y=change in x: (y+Δy)=3(x+Δx)² -7(x+Δx)-4 Subtract y from both sides: y+Δy-y=3(x² +2xΔx+Δx²)-7(x+Δx)-4-y Where y=3x² -3x-4 y+Δy-y=3x²+6xΔx+3Δx²-7x-7Δx-4-(3x² -7x-4) Δy=3x² +6xΔx+3Δx² -7x-7Δx-4-3x²+7x+4 Δy=6xΔx-7Δx+3Δx² Divide both sides by Δx: Δy/Δx=6xΔx/Δx -7Δx/Δx +3Δx²/Δx Δy/Δx=6x -7 +3Δx Lim(Δy/Δx) =6x-7 +3(0) Δx--> 0 Lim(Δy/Δx) =6x -7 .....Q. E. D Δx-->0 |
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