Approximation
Definition
An approximation is an estimate or close value that is not exact but provides a reasonable representation of something. It involves finding values that are close enough to be useful while acknowledging some degree of error.
Analogy
Imagine you're trying to measure your height using only a ruler with inch markings. Since your height may fall between two consecutive inches, you have to make an approximation by choosing either one inch below or one inch above your actual height.
Related terms
Error Bound: An error bound refers to an upper limit on how much an approximation can deviate from its exact value.
Rounding: Rounding involves approximating numbers by replacing them with simpler or more convenient values while considering their place value.
Taylor Series Expansion: A method used to approximate functions by representing them as infinite sums of terms involving powers of variables.
"Approximation" appears in:
Additional resources (1)
Practice Questions (6)
- In a Riemann sum, as the number of rectangles (n) increases, what happens to the accuracy of the approximation?
- Which of the following statements is true about the error in Euler's method approximation?
- What does the remainder term represent in a Taylor series approximation?
- For the alternating series (-1)^n/(2n+1), what is the error bound for the approximation obtained by using the first 5 terms?
- For the alternating series (-1)^n/(n^3 + 1), what is the error bound for the approximation obtained by using the first 3 terms?
- What happens to the accuracy of a Taylor polynomial approximation as the degree of the polynomial increases?
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