Determine the Following Limits, If They Exist $\lim _{x \rightarrow-2} x(x-2)^{2}$

question 26

Essay

Determine the following limits, if they exist.
(a) $\lim _{x \rightarrow-2} x(x-2)^{2}$
(b) $\lim _{x \rightarrow 3} \frac{x^{2}-7 x+12}{x^{2}-4 x+3}$
(c) $\lim _{x \rightarrow \infty} 5 x-2$
(d) $\lim _{x \rightarrow 0} \frac{\sin 5 x}{x^{2}-x}$
(e) $\lim _{x \rightarrow 3} \frac{x-3}{x^{2}+5}$
(f) $\lim _{x \rightarrow 0} \frac{2}{x}$

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Definitions:

William Harvey

William Harvey was a 17th-century English physician who made groundbreaking contributions to anatomy and physiology, notably describing the circulatory system and the motion of blood in the body.

Astrology

The study of the movements and relative positions of celestial bodies interpreted as having an influence on human affairs and the natural world.

Nonscientific Belief

A belief system or opinion that is not based on the scientific method or empirical evidence, often found in cultural, religious, or personal beliefs.

Universal Gravitation

The law of physics that states that every particle attracts every other particle in the universe with a force that is direct between the masses and inversely proportional to the square of the distance between their centers.