Answer
($\sqrt 15$, $\sqrt 17$) and 𝛿 = 0.1231
Work Step by Step
Solve the inequality |f(x) -L| < e
|$x^{2}$ - 5-11| <1
-1 x > $\sqrt 17$
or $\sqrt 15$< - x < $\sqrt 17$
-$\sqrt 15$< x < -$\sqrt 17$
Since we need interval about c=4, required interval is($\sqrt 15$, $\sqrt 17$)
Find a value of 𝛿>0;
Now we need to find the value of 𝛿>0 that places the open interval
(4-𝛿, 4+𝛿) centered at 4 inside the interval ($\sqrt 15$, $\sqrt 17$). distance between 4and $\sqrt 15$ is 0.12702 and distance between 4 and $\sqrt 17$ is]0.1231. so we will take the smaller value for 𝛿, so 𝛿 = 0.1231
