Answer
( - 1.111, -0.909) and 𝛿 = 0.091
Work Step by Step
Solve the inequality |f(x) -L| < e
|$\frac{1}{x}$ + 1| <0.1
-0.1 x > $-0.9^{-1}$
or - 1.1110;
Now we need to find the value of 𝛿>0 that places the open interval
(-1-𝛿, -1+𝛿) centered at -1 inside the interval ( -1.111, -0.909). distance between -1 and -1.111, is 0.111 and distance between-1 and -0.909 is 0.091. so we will take the smaller value for 𝛿, so 𝛿 = 0.091
