Question

Find the indicated limit, if it exists.

limit of f of x as x approaches 8 where f of x equals x plus 10 when x is less than 8 and f of x equals 10 minus x when x is greater than or equal to 8

Answer 1

since the function is divided up at x=8
and both pieces are continuous on the given intervals
you find the left and right limit by just plugging in 8 into the pieces

if they are the same the limit exist and is what both left and right limit agreed to

if they are different the limit doesn't exist