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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
 4 months ago
 4 months 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
 4 months ago
 4 months ago

This Question is Closed

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

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

cptBest ResponseYou've already chosen the best response.1
What should I do after that? Add those two equations together?
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
You will have a system of equations to solve just like from algebra class.
 4 months ago

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

myininayaBest 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?
 4 months ago

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

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

cptBest 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?
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
It isn't approaching 2. It is approaching 2.
 4 months ago

myininayaBest 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.
 4 months ago

cptBest 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?
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
Have you ever solved a system of two linear equations?
 4 months ago

cptBest ResponseYou've already chosen the best response.1
Yes, like 4 years ago haha.
 4 months ago

cptBest 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) ?
 4 months ago

myininayaBest 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.
 4 months ago

myininayaBest 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.
 4 months ago

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

myininayaBest ResponseYou've already chosen the best response.1
Do you think you can rewrite equation 2 in that form?
 4 months ago

cptBest ResponseYou've already chosen the best response.1
32a  4b = 8 ( 2nd equation right) right?
 4 months ago

myininayaBest ResponseYou've already chosen the best response.1
So we have 16a4b=16 32a4b=8
 4 months ago

myininayaBest 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.
 4 months ago

myininayaBest 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)
 4 months ago

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

cptBest ResponseYou've already chosen the best response.1
I got the final answer of 6 for b. Is that right?
 4 months ago

cptBest ResponseYou've already chosen the best response.1
yayyy, you should just be my tutor haha. Thank you so much :D
 4 months ago
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