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Review,Calculus 1

Absolute values

• Suppose a > 0, then

|x| = a if and only if x = ±a,
|x| < a if and only if −a < x < a,
|x| > a if and only if x > a or x < −a.

Laws of exponents

Natural logarithm

• ln(x) = y if and only if ey = x,

• ln(xy) = ln(x) + ln(y),

• ln(x/y) = ln(x) + ln(y),

• ln(x2) = a ln(x)

Trigonometry

Equations of lines

• The slope of a nonvertical line that passes through the points (x1, y1) and (x2, y2)
is
.
The slope of a vertical is not defined.

• Point- slope form of the equation of a line : An equation of the line passing
through the point (x1, y1) and having slope m is
y − y1 = m(x − x1).

Slope - intercept form of the equation of a line: An equation of the line with
slope m and y - intercept b is
y
= mx + b.

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