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 one year ago
If f(x) is continuous and differentiable and f(x) = ... then b?
f(x) =
{ax^4 + 5x, x< or = 2
{bx^2  3x, x> 2,
then b = ?
Help pls
 one year ago
If f(x) is continuous and differentiable and f(x) = ... then b? f(x) = {ax^4 + 5x, x< or = 2 {bx^2  3x, x> 2, then b = ? Help pls

This Question is Closed

myininaya
 one year ago
Best ResponseYou've already chosen the best response.11st set these two expressions equal to each other: \[\lim_{x \rightarrow 2^}f(x)=\lim_{x \rightarrow 2^+}f(x)\]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.12nd set these two expressions equal to each other: \[\lim_{x \rightarrow 2^}f'(x)=\lim_{x \rightarrow 2^+}f'(x)\]

cpt
 one year ago
Best ResponseYou've already chosen the best response.1What should I do after that? Add those two equations together?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1You will have a system of equations to solve just like from algebra class.

cpt
 one year ago
Best ResponseYou've already chosen the best response.1Well I got, 4a  10 = 4b  6 and then 32 + 5 = 4b  3. Is that correct?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1The first equation on the left hand side you have 4a10 I think it should be 16a+10. What happen to a in the second expression?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1\[a(2)^4+5(2)=b(2)^23(2) \text{ first equation }\]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1\[4a(2)^3+5=2b(2)3 \text{ second equation }\]

cpt
 one year ago
Best ResponseYou've already chosen the best response.1Wait isn't it a(2)^4 + 5 (2) since the limit is coming from the left side?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1It isn't approaching 2. It is approaching 2.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1You have the left is just approaching 2 from the left. You have the right is just approaching 2 from the right. Either way they are both still approaching 2 and not some other number.

cpt
 one year ago
Best ResponseYou've already chosen the best response.1Ahh ok I got it :) After I get these 2 equations then what should I do afterward?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1Have you ever solved a system of two linear equations?

cpt
 one year ago
Best ResponseYou've already chosen the best response.1Yes, like 4 years ago haha.

cpt
 one year ago
Best ResponseYou've already chosen the best response.116a + 10 4b  6 32a + 5 4b  3 ( Can't I just substitute it and then solve it) ?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1You can put them both in ax+by=c form if you want. Like if we had something like 2x+3y=1 2x+3y=1 This system is already set up for elimination. Add the equations together and solve for y first would be my strategy. 6y=2 y=2/6=1/3 Then plug into one of the other equations and solve for x.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1Or this system: 3x6y=2 x+y=2 This one isn't set up for elimination. But you could multiply the bottom equation by 3 so we would have it setup for elmination. 3x6y=2 3x3y=6 add 9y=4 y=4/9 and then so on to find x.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1\[a(2)^4+5(2)=b(2)^23(2) \text{ first equation }\] \[16a+10=4b6\] \[16a4b=16 \text{ rewrote the equation 1} \]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1Do you think you can rewrite equation 2 in that form?

cpt
 one year ago
Best ResponseYou've already chosen the best response.132a  4b = 8 ( 2nd equation right) right?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1So we have 16a4b=16 32a4b=8

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1If we multiply the second or even the first (just not both of them) by 1, then we can set this up for elimination method.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1I'm trying to eliminate b. (you could go for a but I prefer working with smaller numbers)

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1So 16a+4b=16 32a4b=8 add the equations together and what do we get?

cpt
 one year ago
Best ResponseYou've already chosen the best response.1I got the final answer of 6 for b. Is that right?

cpt
 one year ago
Best ResponseYou've already chosen the best response.1yayyy, you should just be my tutor haha. Thank you so much :D
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