Find $$\lim _ { x \rightarrow 6 } \frac { \sqrt { x + 7 } } { x - 2 }$$

question 40

Multiple Choice

Find
$$\lim _ { x \rightarrow 6 } \frac { \sqrt { x + 7 } } { x - 2 }$$
by direct substitution.

• A) \(\frac { \sqrt { 6 } } { 4 }\)
• B) \(\frac { \sqrt { 13 } } { 2 }\)
• C) \(\frac { \sqrt { 13 } } { 4 }\)
• D) \(\frac { 1 } { 4 }\)
• E) \(\sqrt { 13 }\)

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Definitions:

Modus Tollens (MT)

A form of logical argument where, from "If P then Q" and "Not Q," it follows that "Not P."

Atomic Sentences

Simple sentences that cannot be divided into smaller meaningful elements within a logical structure.

Truth Table

A diagram in logic used to determine the validity of a proposition by listing all possible scenarios and their outcomes.

Modus Ponens (MP)

A logical argument form that asserts if a conditional statement ("if p then q") is accepted, and the antecedent (p) holds, then the consequent (q) must also hold.