Calculus

Simona Riva

Collection of Calculus worksheets.

Table of Contents

  1. Functions
    1. Domain and range - Exploration
    2. Periodic Functions
  2. Limits and Continuity
    1. Finite limit of f(x) when x tends to a finite value - Lesson+Practice
    2. Infinite limit of f(x) when x tends to infinity - Lesson+Practice
    3. Finite Limit of f(x) When x Tends to Infinity - Lesson+Practice
    4. Infinite Limit of f(x) When x Tends to a Finite Value - Lesson+Practice
    5. Non-uniform continuity of 1/x - Exploration
  3. Derivatives
    1. Geometrical meaning of the derivative - Lesson+Practice
    2. Exploring the Derivative of a Quadratic Function
    3. Exploring the Derivative of an Exponential Function
    4. Rolle's Theorem - Lesson+Exploration+Practice
    5. Optimal boxes - Practice
  4. Areas and Volumes
    1. Solids of revolution - Disk integration - Exploration+Practice

1.

Functions

  • 1. Domain and range - Exploration
  • 2. Periodic Functions

1.1.

Domain and range - Exploration

In the app below, select the property that you want to explore, then follow the instructions.[br][br]The small points on the function graph allow you to change its shape.
A matter of existence...
We know that:[br]- polynomials exist for any value of the variable[br]- fractions exist if their denominators are non-zero[br]- roots with an even index exist if their radicands are non-negative[br]- roots with an odd index exist for all values of the radicand[br][br]If the analytical expression of a function contains more "parts" that need conditions to exist, then the function exists for all values of the variable that satisfy all these conditions.
Do the functions [math]f\left(x\right)=\sqrt{x^2+5x+6}[/math] and [math]g\left(x\right)=\frac{1}{\sqrt{x^2+5x+6}}[/math] have the same domain?[br]Explain your conjecture, than calculate the domain(s) of [math]f\left(x\right)[/math] and [math]g\left(x\right)[/math].
What is the domain of [math]h\left(x\right)=\left|x+7\right|+1[/math]?[br]And the range?
– Simona Riva

1.2.

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2.

Limits and Continuity

  • 1. Finite limit of f(x) when x tends to a finite value - Lesson+Practice
  • 2. Infinite limit of f(x) when x tends to infinity - Lesson+Practice
  • 3. Finite Limit of f(x) When x Tends to Infinity - Lesson+Practice
  • 4. Infinite Limit of f(x) When x Tends to a Finite Value - Lesson+Practice
  • 5. Non-uniform continuity of 1/x - Exploration

2.1.

Finite limit of f(x) when x tends to a finite value - Lesson+Practice

The predefined definition in the app is the [math]\varepsilon-\delta[/math] .[br]The button at the bottom right of the app allows you to toggle between this definition and the definition based on neighborhoods.[br][br]Explore the definition step by step, then drag the slider and move point [math]x[/math] to view the values of [math]f\left(x\right)[/math] in the interval in which the limit holds.
Apply the definition and state which of the following limits are correct:
– Simona Riva

2.2.

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2.3.

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2.4.

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2.5.

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3.

Derivatives

  • 1. Geometrical meaning of the derivative - Lesson+Practice
  • 2. Exploring the Derivative of a Quadratic Function
  • 3. Exploring the Derivative of an Exponential Function
  • 4. Rolle's Theorem - Lesson+Exploration+Practice
  • 5. Optimal boxes - Practice

3.1.

Geometrical meaning of the derivative - Lesson+Practice

Explore the geometrical construction of the derivative of a function at a (draggable) point [color=#1e84cc][b][i]P[/i][/b][/color].[br][br]The slider [b][color=#1e84cc][i]h[/i][/color][/b] represents the independent variable increment.
Apply the definition to calculate the derivatives of the following functions, at the given points:[br][br][math]f(x)=\sqrt{3x-1} \mbox{ at } x=3[/math][br][br][math]f(x)=e^{2x} \mbox{ at } x=0[/math][br][br][math]f(x)=\frac{1}{1-x} \mbox{ at } x=2[/math]
– Simona Riva

3.2.

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3.3.

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3.4.

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3.5.

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4.

Areas and Volumes

  • 1. Solids of revolution - Disk integration - Exploration+Practice

4.1.

Solids of revolution - Disk integration - Exploration+Practice

Explore solids of revolution formed by revolving a plane region about the [i]x[/i]-axis or the [i]y[/i]-axis.[br][br]Move the [b][color=#6aa84f][i]green points[/i][/color][/b], and use the sliders to select which solid you want to explore.[br]Use the [b][color=#1e84cc][i]angle slider[/i][/color][/b] to rotate the region manually, or select [b][i]Rotate![/i][/b] in the drop-down list.[br][i]D[/i][i]rag [/i]the 3[i]D View[/i] to explore the solid from different points of view.[br][br]The current value of the volume is displayed only for revolutions about the [i]x[/i]-axis.
– Simona Riva

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