Question

DSDFSDGDSG

Answer 1

@phi @Compassionate @Loser66 @jim_thompson5910

Answer 2

plug x = 2 into cx^2+4x to get ???

Answer 3

4c+8

Answer 4

plug x = 2 into x^3-cx to get ???

Answer 5

8-2c

Answer 6

set the two expressions equal to each other and solve for c

Answer 7

c=0

Answer 8

thank you so much! could you help me with a similar problem? i think i now know how to do it but i could still use help

Answer 9

go ahead

Answer 10

so would you plug in 2 for the first two equations and plug in 3 into the second two?

Answer 11

you are correct

Answer 12

ok. the first equation is undefined at 2

Answer 13

actually, yeah I just realized that lol, hmm let me think

Answer 14

no wait

Answer 15

x^2 - 4 factors to (x-2)(x+2)

Answer 16

then the x-2 terms will cancel

Answer 17

but its still undefined. that doesnt change

Answer 18

there's a removable discontinuity at x = 2 for (x^2-4)/(x-2)

Answer 19

yes. there is

Answer 20

basically there's a hole there

to make things continuous, we need to see what values of a & b will make the second piece connect to the first

Answer 21

(x^2-4)/(x-2) simplifies to x+2

so when x = 2, x+2 becomes 4

Answer 22

then we plug x = 2 into ax^2-bx-8 to get 4a-2b-8

Answer 23

We want this to equal 4 so the first and second pieces connect

4a-2b-8 = 4

Answer 24

Now we plug x = 3 into the second piece to go from ax^2-bx-8 to 9a-3b-8

and we plug x = 3 into the third piece to go from 6x-a+b to 18-a+b

we can now say

9a-3b-8 = 18-a+b

Answer 25

so the goal is to now solve this system of equations

4a-2b-8 = 4
9a-3b-8 = 18-a+b

Answer 26

a=1 and b=-4?

Answer 27

correct

Answer 28

thank you sooooo much!!!

Answer 29

you're welcome