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Calculus Pre Process Tool \hspace{2.2in} {\it Raising Calculus to the Surface}
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Calculus Pre Process Tool \hspace{2.2in} {\it Raising Calculus to the Surface}
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\begin{enumerate}
\item Suppose the result of $\int_a^b q(x) \; dx $ is a real number, $k$. Explain what $k$ means and how it was measured. Sketch any images you have in mind in the space below.
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\item Suppose that a function $G$ is defined: $G = \int_a^t f(x) \; dx$
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\item Is $G$ a function of $t$ or a function of $x$? Justify your response.
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\item Now suppose that you increase the value of $t$. What would you need to know about the function $f$ to determine if $G$ increases or decreases?
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Calculus Pre Process Tool \hspace{2.2in} {\it Raising Calculus to the Surface}
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\item If $f(x) = 3x^3 -6x^2 - 3x - 1$
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\item Determine the equation of the linear approximation $L(x)$ at $x=2$. What is the relationship between $f(x)$ and $L(x)$?
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\item Describe the behavior of the function $L(x)$ and its associated graph.
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\item At the $x$-value of $1.8$, the error of the approximation is $.456$. What does the $.456$ mean and why does it occur?
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\end{enumerate}
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Calculus Pre Process Tool \hspace{2.2in} {\it Raising Calculus to the Surface}
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\item A function $f(x)$ is defined for all $x$ greater than or equal to zero.
Describe all the ways you would use for finding the maximum or minimum values of the function. How do you know whether $f(x)$ has a maximum or minimum at a point?
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\item Suppose you have a function $f$ of one variable.
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\item What does it mean for $f$ to have a rate of change of $1.65$ for a value of $x=a$? What information do you need to know to determine this value?
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\item If you were to explain to someone how to determine the rate of change of a one variable function, what would you say?
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Calculus Pre Process Tool \hspace{2.2in} {\it Raising Calculus to the Surface}
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\item Consider the phrase {\it the area of a circle is a function of its circumference}.
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\item Please explain the meaning of this phrase.
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\item What values are in the domain of this function? What are possible units for these values?
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\item Create a symbolic representation of this function.
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\item Suppose $f(x)$ is a function. Describe the relationship between this function and $f(x+2)$.
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Calculus Pre Process Tool \hspace{2.2in} {\it Raising Calculus to the Surface}
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\item What is a function?
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\item What is a derivative?
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\item What is an integral?
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\end{enumerate}