Question

Please help!!!!!
Find a value for k in the function below so that the function is continuous at all points.
h(x)={(x^7+1/x+1) x≠-1
k x=-1

Answer 1

Do you know what the value of k=?

Answer 2

yes...

Answer 3

can you simplify this: \(\large \frac{x^7+1}{x+1} \) ???

Answer 4

no

Answer 5

do you know synthetic division?

Answer 6

No

Answer 7

do you know how to do long division?

Answer 8

yes

Answer 9

*of polynomials??

Answer 10

maybe

Answer 11

ok... first i'd like you to see what the answer will be if we graph it... we can do the algebra (long division) later...
here is an online graphing calculator.... can you graph: y=\(\large \frac{x^7+1}{x+1} \) ??

Answer 12

https://www.desmos.com/calculator

Answer 13

I have a graphiong calculator and I graphed it and got it.

Answer 14

so what do you think k = ??? when x=-1?

Answer 15

k=-1

Answer 16

or k=0

Answer 17

no... what is the y-value when x=-1? look at your graph....

Answer 18

here's a screen shot :

Answer 19

k=0

Answer 20

no.... at x=-1, the y-value on the graph is not 0....

Answer 21

I have an error for the y value so that is why I'm a little confused

Answer 22

yes... you should have an error because the function is not defined at x=-1. but if you look at the graph, at x values close to x=-1, what does the y values seem to be close to?

Answer 23

k=1

Answer 24

If you want to show it without the use of a graph, you'll have to find the quotient, like @dpalnc mentioned.

Then, to show continuity at x = -1, you have to find k such that
\[\lim_{x\to -1}h(x)=k,\text{ i.e.}\\
\lim_{x\to -1}\frac{x^7+1}{x+1}=k\]

Answer 25

so does k=-1 really confused?

Answer 26

no... k is NOT -1

Answer 27

ok well i'm really confused and don't get it so I NEED HELP

Answer 28

Well do you know what continuity means?

Answer 29

no

Answer 30

There's your problem. Brush up on the definition of continuity first, then come back.

Answer 31

ok got it