General Binomial Expansion (AQA A-Level Mathematics): Quizzes

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Approximating Values
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What is 5.67895.6789 rounded to two decimal places?

5.685.68

What is 3.63.6 rounded to the nearest integer?

44

What is 5.67895.6789 truncated to two decimal places?

5.675.67

How does truncation differ from rounding?

It drops digits without rounding up

What is 0.0045670.004567 to three significant figures?

0.004570.00457

What is 123,456123,456 to three significant figures?

123,000123,000

What is the linear approximation formula for f(x)f(x) near x=ax = a?

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

Using linear approximation, what is 4.1\sqrt{4.1} approximately?

2.0252.025

What is the binomial approximation for (1+x)n(1 + x)^n when xx is small?

1+nx1 + nx

What is the Taylor series approximation for exe^x near x=0x = 0?

1+x+x22!1 + x + \frac{x^2}{2!}

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