Arithmetic and Geometric and Harmonic Sequences

Derivatives

Functions-Derivatives-Integrals

Integrals

L'Hôpital's Rule

Limit of a Function

Ordered Pair

Sequences

Sigmoid Function

This will take an arithmetic series or geometric series or harmonic series, and an optional amount (n), and determine the following information about the sequence

1) Explicit Formula

2) The remaining terms of the sequence up to (n)

3) The sum of the first (n) terms of the sequence Also known as arithmetic sequence, geometric sequence, and harmonic sequence

Calculator · Watch the Video1) Explicit Formula

2) The remaining terms of the sequence up to (n)

3) The sum of the first (n) terms of the sequence Also known as arithmetic sequence, geometric sequence, and harmonic sequence

Derivatives

This lesson walks you through the derivative definition, rules, and examples including the power rule, derivative of a constant, chain rule

LessonFunctions-Derivatives-Integrals

Given a polynomial expression, this calculator evaluates the following items:

1) Functions ƒ(x). Your expression will also be evaluated at a point, i.e., ƒ(1)

2) 1^{st} Derivative ƒ'(x) The derivative of your expression will also be evaluated at a point, i.e., ƒ'(1)

3) 2^{nd} Derivative ƒ''(x) The second derivative of your expression will be also evaluated at a point, i.e., ƒ''(1)

4) Integrals ∫ƒ(x) The integral of your expression will also be evaluated on an interval, i.e., [0,1]

5) Using Simpsons Rule, the calculator will estimate the value of ≈ ∫ƒ(x) over an interval, i.e., [0,1]

Calculator1) Functions ƒ(x). Your expression will also be evaluated at a point, i.e., ƒ(1)

2) 1

3) 2

4) Integrals ∫ƒ(x) The integral of your expression will also be evaluated on an interval, i.e., [0,1]

5) Using Simpsons Rule, the calculator will estimate the value of ≈ ∫ƒ(x) over an interval, i.e., [0,1]

Integrals

This lesson walks you through the integral definition, rules, and examples

LessonL'Hôpital's Rule

This lesson walks you through L'Hôpitals's Rule including the definition, pronunciation, notation, and examples

LessonLimit of a Function

This lesson walks you through what limit is, how to write limit notation, and limit theorems

LessonOrdered Pair

This calculator handles the following conversions:

* Ordered Pair Evaluation and symmetric points including the abcissa and ordinate

* Polar coordinates of (r,θ°) to Cartesian coordinates of (x,y)

* Cartesian coordinates of (x,y) to Polar coordinates of (r,θ°)

* Quadrant (I,II,III,IV) for the point entered.

* Equivalent Coordinates of a polar coordinate

* Rotate point 90°, 180°, or 270°

* reflect point over the x-axis

* reflect point over the y-axis

* reflect point over the origin

Calculator* Ordered Pair Evaluation and symmetric points including the abcissa and ordinate

* Polar coordinates of (r,θ°) to Cartesian coordinates of (x,y)

* Cartesian coordinates of (x,y) to Polar coordinates of (r,θ°)

* Quadrant (I,II,III,IV) for the point entered.

* Equivalent Coordinates of a polar coordinate

* Rotate point 90°, 180°, or 270°

* reflect point over the x-axis

* reflect point over the y-axis

* reflect point over the origin

Sequences

Given a function a(n) and a count of sequential terms you want to expand (n), this calcuator will determine the first (n) terms of your sequence, {a_{1}, a_{2}, ..., a_{n}}

CalculatorSigmoid Function

Calculates the Sigmoid Function S(x) given an x value

Calculator · Watch the Video