General Binomial Expansion (Edexcel A-Level Mathematics): Flashcards

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Approximating Values
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What is the purpose of approximating values in maths?

To simplify calculations or estimate complex functions.

How does rounding work in approximating values?

Adjusts a number to the nearest specified value.

What is truncation in approximation?

Cutting off digits without rounding them up.

What are significant figures used for?

To indicate the precision of a measured value.

What is linear approximation based on?

Using the tangent line at a point on a curve.

What does binomial approximation simplify?

Expressions of the form (1+x)n(1 + x)^n for small xx.

What does Taylor series approximation do?

Expands a function into an infinite sum of terms.

Example of rounding to one decimal place for 5.67895.6789?

5.75.7 is the result when rounded to one decimal place.

How do you truncate 5.67895.6789 to two decimal places?

Truncated value is 5.675.67 when cut off at two decimal places.

What is the formula for linear approximation?

f(x)f(a)+f(a)(xa)f(x) ≈ f(a) + f'(a)(x - a).

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