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Discussion Sheet 9: Functions and Limits
In this function and limits learning exercise, students identify a one-to-one correspondence and identify an inverse function. They compute limits of functions. This two-page learning exercise contains five multi-step problems.
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The Geometric Interpretation of Partial Derivatives
In this partial derivative worksheet, students compute partial derivatives at a given point. They measure the slope tangent to the surface at the point. This one-page worksheet contains two multi-step problems.
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The Second Derivative Test for Relative Extreme in Three Dimensional Space
In this second derivative worksheet, students determine the relative maximum and minimum values of given surfaces in three-dimensional space. They perform the second derivative test, and identify the partial derivatives. This one-page...
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Worksheet 7: Distance and Rate
In this distance and rate worksheet, students determine the rate in which something is moving, and explore the rate a surface area of a cube is changes under given circumstances. This one-page worksheet contains seven multi-step problems.
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Worksheet 6: Derivative & Slope
In this derivative and slope worksheet, students find the derivative of given equations. They identify the slope of a line tangent to a graph and find the concavity of a graph. This one-page worksheet contains seven multi-step problems.
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Maclaurin Series Quiz
In this Maclaurin series worksheet, students use the Maclaurin series to find the first nonzero terms in a function. They estimate the value of a function with a given absolute error. This two-page worksheet contains two multi-step...
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The Derivative
In this derivative learning exercise, students estimate the derivative of given functions, compute the rate of change at a given point, and simplify the difference quotient. This two-page learning exercise contains definitions,...
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Implicit Differentiation
In this implicit differentiation worksheet, students use the chain rule to solve for the derivative. The find the equation for the tangent line at a given point and determine if the line is vertical. This two-page worksheet contains...
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Differentiability and Linear Approximation
In this differentiability activity, students write expressions for a tangent line approximation to a graph, determine the limits, and use Taylor's theorem to differentiate given functions. This three-page activity contains a discussion...
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Worksheet 14: Integrals
In this integral worksheet, students evaluate integrals and determine the volume of given polygons bounded by graphs. This three-page worksheet contains approximately twenty multi-step problems.
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Worksheet 2: Evaluating Functions
In this function worksheet, students evaluate sums, estimate the area of the region between graphs, estimate the volume of a hemisphere, and use subintervals and the limit definition integrals to evaluate functions. This two page...
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Challenge Sheet 3: Average Value of a Function
For this average value worksheet, students determine the average value of functions, sketch graphs of continuous intervals, evaluate integrals, find the average value of a function and convert limits to a definite integral. This...
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Challenge Sheet 7: Area and Cross-Sections
In this area activity, students set up integrals which evaluate the area of a region bounded by graphs. they use vertical and horizontal cross-sections. This two-page activity contains seven multi-step problems.
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Quiz 1: Sums
For this sums worksheet, students evaluate sums. They use the limit definition of the definite integral to evaluate a function. This two-page worksheet contains four multi-step problems.
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Volume of 3-D Figures
In this volume worksheet, students compute the volume of 3-D figures bounded by graphs. They identify a solid formed by rotation about a given line. Students use the Disc Method and the Shell Method to make their computations. This...
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Area of Cross-Sections
In this area worksheet, students find the area of regions bounded by graphs. They set up integral equations for determining the vertical cross-section and the horizontal cross-section of a given figure. This one-page worksheet contains...
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Functions and Slopes
In this function worksheet, students find the slope of a line tangent to a given graph, they derive formulas for the area and perimeter of a given right triangle, they graph functions, and compute the derivative of functions. This...
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Continuous Functions
In this continuous function worksheet, students determine the average velocity of objects over given intervals of time. They compute the derivative of functions and determine the slope of a line. This four-page worksheet contains...
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Instantaneous Velocity
In this velocity worksheet, students determine the average and instantaneous velocity. They compute the derivative of given functions. This one-page worksheet contains seven multi-step problems.
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Domain & Range of Functions
In this function worksheet, students determine the domain and range of given functions. They identify terms in a sequence of integers, This two-page worksheet contains seven multi-step problems.
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Worksheet 13: Slope and Concavity
In this function worksheet, students determine the equation of a line, compute slope and concavity of a graph, and find the maximum volume of three-dimensional figures. This one-page worksheet contains six multi-step problems.
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Worksheet 14 1/2: Newton's Method
In this Newton's Method worksheet, students use Newton's Method to estimate the largest root and sketch graphs. This one-page worksheet contains six multi-step problems.
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Worksheet 10: Differentiation
In this differentiation learning exercise, students differentiate functions, sketch graphs of functions, determine the area of inscribed polygons, and use the Mean Value Theorem for functions and intervals. This four-page learning...
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The Integral Test
In this integral test, students determine the limits, give partial sums of infinite series, explore geometric series, and use the Integral Test to determine if a function converges. This two-page learning exercise contains six...