Question

Lim f(x) = 19, find the value of A and B, if the lim f(x) = Ax – 3B and lim f(x) = **+ B

X
1
A is
B is

Question is messed up so a photo of the question is below. Thanks in advance

Answer 1

A = 4, B = 3

Explanation:

In order for the limit to exist and have a value of 19, the left limit and the right limit must both have that value at x=7.

left limit = 19

right limit = 19

__

4A(7)/7 +B = 19

A(7) -3B = 19

Adding 3 times the first equation to the second gives ...

3(4A +B) +(7A -3B) = 3(19) +(19)

19A = 4(19) . . . . . simplify

A = 4 . . . . . . . . divide by 19

Substituting into the first equation gives ...

4(4) +B = 19

B = 3 . . . . . . . subtract 16

A is 4, B is 3.