Calculus is the mathematics that describes changes in functions. In this chapter, we review all the functions necessary to study calculus. We define polynomial, rational, trigonometric, exponential, and …

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In precalculus, you learned a formula for the position of the maximum or minimum of a quadratic equation 𝑦 = 𝑎 𝑥 2 + 𝑏 𝑥 + 𝑐, y = a x 2 + b x + c, which was ℎ = − 𝑏 (2 𝑎) h = b (2 a) Prove this formula using …

For the following exercises, solve using calculus, then check your answer with geometry. 56. Determine the equations for the sides of the square that touches the unit circle on all four sides, as seen in the …

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Toward the end of the twentieth century, the values of stocks of internet and technology companies rose dramatically. As a result, the Standard and Poor...

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