Question

http://prntscr.com/88wnz4
ap calc ab

Answer 1

So you need your answer checked? Or you also need an explanation?

Answer 2

i accidentally checked the first one. an explanatoion would be great@

Answer 3

have you learned about left hand limits? and right hand limits?

Answer 4

yes

Answer 5

so you know what this notation means?

\[\LARGE \lim_{x \to 1^{-}} f(x)\]

Answer 6

yes the limit is approaching 1 from the left side

Answer 7

correct

Answer 8

which piece will be used here? the x^2 + 4 piece? or the x+4 piece?

Answer 9

x^2+4

Answer 10

yes because f(x) = x^2 + 4 if x < 1

Answer 11

so what we do is simply plug in x = 1 to get

f(1) = 1^2 + 4 = 1+4 = 5

as x gets closer and closer to 1 from the left side, the limiting value is 5

in other words,

\[\LARGE \lim_{x \to 1^{-}} f(x) = 5\]

Answer 12

so it would be c because it doesn't equal 1?

Answer 13

well let's compute the right hand limit

Answer 14

do you know how to do so?

Answer 15

The limit as x approaches 1 from the right side and plus in x=1 into x+4 ?

Answer 16

yes because f(x) = x+4 when x > 1

Answer 17

plug in*

Answer 18

ok ill try it

Answer 19

It also = 5 from the right side

Answer 20

yes,

\[\LARGE \lim_{x \to 1^{+}} f(x) = 5\]

Answer 21

because f(1) is defined, and because the left and right hand limits equal the same value, this means f(x) is continuous at x = 1. It's continuous everywhere else because the two pieces are polynomials. All polynomials are continuous.

Answer 22

so then it would be continuous

Answer 23

actually wait...f(1) isn't defined

Answer 24

I'm not thinking

Answer 25

the piecewise function is set up in a way where x = 1 is left out

Answer 26

notice how there are NO underlines under the > or the <

Answer 27

Ohh i didnt notice that either

Answer 28

f(x) = x^2 + 4 if x < 1

OR

f(x) = x + 4 if x > 1

but what if x = 1 ? The function doesn't say, so f(1) is undefined

Answer 29

Okay, thank you for explaing this problem i appreciate it!

Answer 30

you're welcome