Find the indicated limit, if it exists. 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 …

Question

asked Jan 2, 2019 173k views

1 Answer

Kasper P · Answer 1 · 2019-01-08T07:52:32+0000

Answer:

answer is 7

Explanation:

We are given a piecewise function which has a split at x=0

f(x) =
$f(x) = 7-x^2, x<0\\      = 7, x=0\\      = 10x+7, x>0$

To find the limit, we have to find here left hand limit and right hand limit separately.

Here left hand limit for x tending to 0 is

limit of
7-x^2 as x tends to 0

= 7-0 = 7

Right limit = limit of 10x+7 as x tends to 0

=10(0)+7 = 7

Since right hand limit = left hand limit we have

there exists a limit for x=0 and the limit is 7