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) $\lim _ { h \rightarrow - 4 } \frac { x ^ { 3 } + 64 } { x + 4 }$

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Definitions:

Parol Evidence Rule

A legal principle that prevents parties from presenting extrinsic evidence that contradicts or adds to the written terms of a final contract.

Fair and Accurate Credit Transactions Act

U.S. law enacted to enhance consumer protection and reduce the risk of fraud and identity theft by ensuring accurate credit information.

Statute of Frauds

A legal principle that requires certain types of contracts to be in writing and signed by the involved parties to be enforceable.

Primary Objective Test

A legal standard used to determine the main purpose of a contract or transaction, often applied in tax law to ascertain the primary reason behind a taxpayer's actions.