Determine a Function F and a Number a Where the Given

question 7

Essay

Determine a function f and a number a where the given limit represents the derivative of f at a.(a) $\lim _ { h \rightarrow 0 } \frac { \sqrt { ( 3 + h ) ^ { 2 } - 5 } - 2 } { h }$ (b) $\lim _ { h \rightarrow 0 } \frac { ( 6 + h ) ^ { 2 } - 5 ( 6 + h ) - 11 - 55 } { h }$ (c) $\lim _ { x \rightarrow 0 } \frac { 3 e ^ { x } - 3 } { x }$ (d) $\lim _ { h \rightarrow - 4 } \frac { x ^ { 3 } + 64 } { x + 4 }$

---

Definitions:

Accounts Receivable Turnover

A financial ratio that measures how efficiently a company collects revenue from its credit sales, by dividing net credit sales by the average accounts receivable.

Days' Sales

An indicator of a company's efficiency in managing its inventory, it calculates the number of days it typically takes to sell the entire inventory.

Average Accounts Receivable

The mean value of accounts receivable over a given period, indicating the average amount owed to a company by its customers.

Inventory Turnover

A measure of how often a company's inventory is sold and replaced over a certain period, indicating the efficiency of inventory management.