Evaluate the function

ƒ(n) = n

at ƒ(0)

Given ƒ(n) = n

Determine the derivative ∫ƒ(n)

Given ƒ(n) = n

Determine the 2nd derivative ∫ƒ(n)

Given ƒ(n) = n

Determine the integral ∫ƒ(n)

Go through and integrate each term

Given the equation ƒ(n) = n

use Simpsons Rule with n =

over the interval [0,1]

ƒ(0) = (0)

ƒ(0) = 0

For this term, a = 1, n = 52

and n is the variable we derive

ƒ'(n) = n

ƒ'(n)( = 1 * 52)n

ƒ'(n) = 52n

For this term, a = 52, n = 51

and n is the variable we derive

ƒ''(n) = 52n

ƒ''(n)( = 52 * 51)n

ƒ''(n) = 2652n

For this term, a = 2652, n = 50

and n is the variable we derive

ƒ

ƒ

ƒ

For this term, a = 132600, n = 49

and n is the variable we derive

ƒ

ƒ

ƒ

ƒ

ƒ

itarget = 0,1

Given ƒ(n) = n

Determine the integral ∫ƒ(n)

Go through and integrate each term

an^{(n + 1)} | |

n + 1 |

= 6497400, n = 48

and n is the variable we integrate

∫ƒ(n) = | 6497400n^{(48 + 1)} |

48 + 1 |

∫ƒ(n) = | 6497400n^{49} |

49 |

Simplify our fraction.

Divide top and bottom by 49

∫ƒ(n) = 132600n

∫ƒ(1) = 6497400(1)132600(1)

∫ƒ(1) = 132600

∫ƒ(1) =

∫ƒ(0) = 6497400(0)132600(0)

∫ƒ(0) = 0

∫ƒ(0) =

∫ƒ(n) on the interval [0,1] = 132600 - 0

ƒ(0) = **0**

ƒ^{(4)}(0) = **0**

∫ƒ(n) on the interval [0,1] =**132600**

ƒ

∫ƒ(n) on the interval [0,1] =

ƒ(0) = **0**

ƒ^{(4)}(0) = **0**

∫ƒ(n) on the interval [0,1] =**132600**

ƒ

∫ƒ(n) on the interval [0,1] =

Free Functions-Derivatives-Integrals Calculator - 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]

This calculator has 7 inputs.

1) 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]

This calculator has 7 inputs.

- derivative
- rate at which the value y of the function changes with respect to the change of the variable x
- exponent
- The power to raise a number
- function
- relation between a set of inputs and permissible outputs

ƒ(x) - functions-derivatives-integrals
- integral
- a mathematical object that can be interpreted as an area or a generalization of area
- point
- an exact location in the space, and has no length, width, or thickness
- polynomial
- an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
- power
- how many times to use the number in a multiplication

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