Limits and Derivatives

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Limits and Derivatives

Limit Laws

Quotient Law

Limit of a quotient is the quotient of the limits(if the limit of the denominator is not 0)

Product Law

Limit of a product is the product of the limits

Constant Multiple Law

Limit of a constant times a function is the constant times the limit of the function

Difference Law

Limit of the difference is the difference of the limits

Sum Law

Limit of the sum is the sum of the limits

Derivatives

Horizontal Tangents then f'(x)=0

f'(x)=(x, f(x)) + estimate slope; f'(x)=(x, f'(x))

Slope change in y over change in x

The function of f' is derived from function of f

Limits at Infinity

The limits at infinity can go in 2 directions depending on the direction the x is traveling on infinity

Negative means x is coming from the left Positive means x is coming from the right

x to infinity grows larger or smaller it approaches a horizontal or vertical asymptote

As x approaches infinity and f(x) equals a number than the function has a horizontal asymptote

As x approaches a number and f(x) is equal to infinity than the function has a vertical asymptote

Tangents

Secant line hits two points on a curve

Point-Slope Formula y-y1=m(x-x1)

Slope of Tangent Line can touch one point on line of a curve

2 points to estimate a slope