Find the Limit $L$ For the Given Function $f$ , the Point $x _ { 0 }$

question 90

Multiple Choice

Find the limit $L$ for the given function $f$ , the point $x _ { 0 }$ , and the positive number $\varepsilon$ . Then find a number $\delta > 0$ such that, for all $x _ { t } 0 < \left| x - x _ { 0 } \right| < \delta \Rightarrow | f ( x ) - L | < \varepsilon$ .
- $$\mathrm { f } ( \mathrm { x } ) = 6 \mathrm { x } + 3 , \mathrm { x } _ { 0 } = - 5 , \varepsilon = 0.06$$

• A) \(\mathrm { L } = - 27 ; \delta = 0.01\)
• B) \(L = - 33 ; \delta = 0.01\)
• C) \(L = - 27 ; \delta = 0.02\)
• D) \(\mathrm { L } = 33 ; \delta = 0.02\)

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Definitions:

AVC

Average Variable Cost, which is the total variable costs of production divided by the quantity of output.

Short Run

A period in which at least one of a firm's inputs is fixed and cannot be varied.

Variable Costs

Expenses that directly fluctuate in accordance with the amount of production or output.

Average Cost

The total cost of production divided by the number of units produced, indicating the cost per unit.