Determine the Following Limits, If They Exist $\lim _{x \rightarrow 4} x(x+4)^{2}$

question 36

Essay

Determine the following limits, if they exist.
(a) $\lim _{x \rightarrow 4} x(x+4)^{2}$
(b) $\lim _{x \rightarrow 1} \frac{x^{2}+3 x-4}{x^{2}-6 x+5}$
(c) $\lim _{x \rightarrow-\infty} 6 x+2$
(d) $\lim _{x \rightarrow 0} \frac{\sin 5 x}{x}$
(e) $\lim _{x \rightarrow 4} \frac{x-4}{x^{2}+2}$
(f) $\lim _{x \rightarrow 0} \frac{2}{x^{2}}$

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Definitions:

Good Continuation

A factor in visual grouping; we tend to perceive contours in a way that alters their direction as little as possible.

Figure-Ground Separation

The visual ability to distinguish an object (the figure) from its surrounding background (the ground).

Feature Detectors

Neurons in the retina or brain that respond to specific attributes of the stimulus, such as movement, orientation, and so on.

Line Orientation

The direction in which a line or linear object points or aligns within a visual field or specified space.