Question

consider the following limit statement:$lim_{x \to -1} (5x + 11) = 6$find the corresponding value of $delta$ when $varepsilon = 0.005$.$delta = -4.995$$delta = 0.001$$delta = 0.01$$delta = -0.01$

Explanation:

Step1: Apply epsilon-delta definition

Start with $|(5x+11)-6| < \varepsilon$
Simplify the left side: $|5x + 5| < \varepsilon$
Factor: $5|x+1| < \varepsilon$

Step2: Isolate $|x+1|$

Divide both sides by 5: $|x - (-1)| < \frac{\varepsilon}{5}$

Step3: Substitute $\varepsilon=0.005$

Calculate $\delta = \frac{0.005}{5}$
$\delta = 0.001$

Answer:

$\boldsymbol{\delta=0.001}$ (Option: $\boldsymbol{\delta = 0.001}$)