Question

For what constant value a is the following function continuous at x= -10 ?

f(x)= (1/x+1/10)/(x+10) when x is not -10
f(x)= a when x= -10

Answer 1

1/x + 1/10 = (x+10)/10x
so, dividing that by x+10, we have
f(x) = 1/(10x) when x ≠ -10

So, if f(x) = a when x = -10, a must be -1/100 to fill in the hole at x = -10.