## lynda.boyce one year ago the cost, c (in millions of dollars) for a software company to seize 50% of an illegal version of a gaming software that they deloped in modeled by the following function c(x)=mx/50-0.5x the value of m is 25. Find the lim x inf-C(x). Explain briefly what this limit means in terms of the given scenario

1. horsegirl27

$$~~~~~~~~~~\LARGE\color{hotpink}{✧}\color{limegreen}{^✯}\color{blue}{_\heartsuit}\color{hotpink}{\diamondsuit}\color{limegreen}{^✧}\color{blue}{\heartsuit}\color{hotpink}{_\star}\color{limegreen}{✧}\color{blue}{^\heartsuit}\color{hotpink}{✯}\color{limegreen}{_\diamondsuit}\color{blue}{^\star}\color{hotpink}{✧}$$ $$~\LARGE\cal\color{hotpink}{W}\color{limegreen}{e}\color{blue}{l}\color{hotpink}{c}\color{limegreen}{o}\color{blue}{m}\color{hotpink}{e}\color{limegreen}{~t}\color{blue}{o}\color{hotpink}{~O}\color{limegreen}{p}\color{blue}{e}\color{hotpink}{n}\color{limegreen}{S}\color{blue}{t}\color{hotpink}{u}\color{limegreen}{d}\color{blue}{y}\color{hotpink}{!}$$ $$~~~~~~~~~~\LARGE\color{hotpink}{✧}\color{limegreen}{^✯}\color{blue}{_\heartsuit}\color{hotpink}{\diamondsuit}\color{limegreen}{^✧}\color{blue}{\heartsuit}\color{hotpink}{_\star}\color{limegreen}{✧}\color{blue}{^\heartsuit}\color{hotpink}{✯}\color{limegreen}{_\diamondsuit}\color{blue}{^\star}\color{hotpink}{✧}$$ $$~~~~~~~~~~~~~~~~~~\Large\cal\color{hotpink}{P}\color{limegreen}{l}\color{blue}{e}\color{hotpink}{a}\color{limegreen}{s}\color{blue}{e}\color{hotpink}{~R}\color{limegreen}{e}\color{blue}{a}\color{hotpink}{d~}\color{limegreen}{t}\color{blue}{h}\color{hotpink}{e}$$ $$~~~~~~~~~~~\href{https:///openstudy.com/code-of-conduct}{\Large\cal{\color{hotpink}{\bigstar~C}}\color{limegreen}{o}\color{blue}{d}\color{hotpink}{e~}\color{limegreen}{o}\color{blue}{f~}\color{hotpink}{C}\color{limegreen}{o}\color{blue}{n}\color{hotpink}{d}\color{limegreen}{u}\color{blue}{c}\color{hotpink}{t}\color{hotpink}{~\bigstar}}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~\Large\cal\color{hotpink}{A}\color{limegreen}{n}\color{blue}{d~}\color{hotpink}{t}\color{limegreen}{h}\color{blue}{e}$$ $$~~\href{https:///openstudy.com/terms-and-conditions}{\Large\cal{\color{hotpink}{\bigstar~T}}\color{limegreen}{e}\color{blue}{r}\color{hotpink}{m}\color{limegreen}{s}\color{blue}{~a}\color{hotpink}{n}\color{limegreen}{d}\color{blue}{~C}\color{hotpink}{o}\color{limegreen}{n}\color{blue}{d}\color{hotpink}{i}\color{limegreen}{t}\color{blue}{i}\color{hotpink}{o}\color{limegreen}{n}\color{blue}{s}\color{hotpink}{~\bigstar}}$$

2. horsegirl27

I'll tag some users who may be able to help you :) @pooja195 @Hayleymeyer @mathmate @Mr_Perfection_xD

3. lynda.boyce

Thank you very much

4. horsegirl27

@casdawson @butterflydreamer @mathstudent55

5. anonymous

Math it up, bruh!

6. lynda.boyce

I am not math smart. I so need help. I can sort of understand algebra but calculus is kicking my bum.

7. anonymous

I love calc! Let me see what I can do, mate!

8. lynda.boyce

thank you so much

9. anonymous

So what exactly do you need?

10. lynda.boyce

I'm trying to understand what this limit means in terms of the given scenario that I had asked about. The cost, C (in millions.... I found the answers to the percentage. but I just don't understand how the answer was reached

11. ganeshie8

thats some very cool latex @horsegirl27 !

12. horsegirl27

Thank you @ganeshie8!! @Whitemonsterbunny17 helped with it!!!

13. ganeshie8

very pretty :D @lynda.boyce is it like this $\large c(x)=\dfrac{mx}{50-0.5x}$

14. lynda.boyce

yes. and then I had to find the cost of seizing 50%. 60%, 70%, 80% and 90% of the illegal software. I found the answers to those. they are200, 300, 466.67, 800, 1800, with M being 100

15. ganeshie8

could you please post the complete question if psble take a screenshot and attach

16. lynda.boyce

17. ganeshie8

So you're fixing $$M=100$$ for part $$b$$ is it

18. lynda.boyce

yes

19. lynda.boyce

but b says to pick a number between 20 and 120

20. ganeshie8

Oops sorry you're correct.

21. ganeshie8

you're working part $$c$$ now ?

22. lynda.boyce

trying to understand it and work it, yes

23. ganeshie8

Look at the graph of C(x) once |dw:1434118083621:dw|

24. ganeshie8

Do you know what $$\large \lim\limits_{x\to100^{\color{red}{-}}}C(x)$$ means ?

25. lynda.boyce

not really. I am very math stupid. it took me forever to understand algebra to pass it

26. ganeshie8

Suppose you're walking on that red line from left hand side of x=100 : |dw:1434118287009:dw|

27. lynda.boyce

ok

28. ganeshie8

As x approaches 100 from left hand side, the graph is shooting up insanely so you will be climbing up higher and higher, yes ? |dw:1434118466475:dw|

29. lynda.boyce

yes

30. ganeshie8

that means it is very Costly to seize all the illegal version

31. lynda.boyce

Going up each percentage, means the cost goes up also

32. ganeshie8

since the cost is increasing without any bounds, we say the cost approaches "infinity" as the percentage approaches 100

33. ganeshie8

mathematically we express it as : $\large \lim\limits_{x\to100^{\color{red}{-}}}C(x) = \color{red}{\infty}$

34. lynda.boyce

so basically, with the infinity, the cost will continue to rise

35. ganeshie8

what exactly do you mean by "with the infinity"

36. lynda.boyce

well infinity is continuous, so no matter what the price increases as the percentage does or even if you get to 100%

37. ganeshie8

Notice that you can never get to seize 100% because it takes "infinite" cost

38. lynda.boyce

so the 100% is always out of reach

39. ganeshie8

Yes, from the graph it is clear that as you seize closer to 100%, the cost shoots up insanely

40. lynda.boyce

I understand that now. thank you very much

41. ganeshie8

np :) btw you seem to be having very good knowledge in algebra

42. lynda.boyce

thank you. sometimes I don't see things as others do, so it's hard to exchange ideas. If that makes any sense....lol

43. ganeshie8

it might be the case that others are not seeing the things you're seeing ;p

44. lynda.boyce

lol, very true