Question

need help on the attached problem

Answer 1

take the limit in the first one see that when you factor and cancel you get
\[x+2\] so the limit is 4

Answer 2

then for the second one you have
\[ax^2-bx+3\] and you now if you replace x by 2 you must get 4 so we have
\[4a-2b+3=4\]
\[4a-2b=1\]

Answer 3

why did you choose to replace x by 2?

Answer 4

oh we are not done. i replaces x by 2 because you know the limit as x goes to 2 of a polynomial is just its value at 2

Answer 5

and we know that the limit must be 4 to match up with the previous function

Answer 6

now replace x by 3 in both the second and third formulas to find another equation in a and b

Answer 7

you get
\[9a-3b+3=6-a+b\] so
\[10a-4b=3\]

Answer 8

now solve
\[4a-2b=1\]
\[10a-4b=3\] get
\[a=b=\frac{1}{2}\]

Answer 9

one question is the reason you knew to use the 2, seeing that x <2? Same question for 3 to, like x greater or equal 3

Answer 10

right. if they are going to be continuous , they have to match up at 2 and 3

Answer 11

ok, thanks!

Answer 12

yw

Answer 13

hey how did you get 1/2 for a and b did you solve it seperately?

Answer 14

no solved the "system" of equations like solving
\[10x-4y=3\]
\[4x-2y=1\]

Answer 15

only you have a and b. like finding the intersection of two lines

Answer 16

I haven't solve problem like that in while how do work that out again?

Answer 17

system of equation