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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
 one year ago
cpt Group Title
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
 one year ago

This Question is Closed

myininaya Group TitleBest ResponseYou've already chosen the best response.1
1st set these two expressions equal to each other: \[\lim_{x \rightarrow 2^}f(x)=\lim_{x \rightarrow 2^+}f(x)\]
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
2nd set these two expressions equal to each other: \[\lim_{x \rightarrow 2^}f'(x)=\lim_{x \rightarrow 2^+}f'(x)\]
 one year ago

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

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

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

myininaya Group TitleBest ResponseYou've already chosen the best response.1
The 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?
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
I mean equation err
 one year ago

cpt Group TitleBest ResponseYou've already chosen the best response.1
oops you are right.
 one year ago

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

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

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

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

myininaya Group TitleBest ResponseYou've already chosen the best response.1
You 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.
 one year ago

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

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

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

cpt Group TitleBest ResponseYou've already chosen the best response.1
16a + 10 4b  6 32a + 5 4b  3 ( Can't I just substitute it and then solve it) ?
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
You 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.
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Or 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.
 one year ago

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

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

cpt Group TitleBest ResponseYou've already chosen the best response.1
32a  4b = 8 ( 2nd equation right) right?
 one year ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
looks good
 one year ago

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

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

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

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

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

myininaya Group TitleBest ResponseYou've already chosen the best response.1
yep. good job.
 one year ago

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