SOLUTION: Find the indicated limit, if it exists.(7 points) limit of f of x as x approaches 0 where f of x equals 7 minus x squared when x is less than 0, 7 when x equals 0, and 10 x plus

Algebra ->  Trigonometry-basics -> SOLUTION: Find the indicated limit, if it exists.(7 points) limit of f of x as x approaches 0 where f of x equals 7 minus x squared when x is less than 0, 7 when x equals 0, and 10 x plus       Log On


   

Question 1139917: Find the indicated limit, if it exists.(7 points)
limit of f of x as x approaches 0 where f of x equals 7 minus x squared when x is less than 0, 7 when x equals 0, and 10 x plus 7 when x is greater than 0
choices below

3

10

7

The limit does not exist.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your 3 equations are:

f(x) = 7 - x^2 when x < 0.

f(x) = 7 when x = 0.

f(x) = 10x + 7 when x > 0

as x approaches 0, 7 - x^2 approaches 7.

as x approaches 0, 10x + 7 approaches 7.

the limit as x approaches 0 is therefore 7.

it's the same value when you approaches it from the left (7 - x^2) as when you approach it from the right (10x + 7).

i'd go with 7.

you can probably see this graphically.

here's what i show.

$$$

all roads point to y = 7 as x approaches, or is at, 0.