General Binomial Expansion (Edexcel 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

Which value does 3.43.4 round to when rounding to the nearest integer?

33

What is 5.67895.6789 when truncated to two decimal places?

5.675.67

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 point aa?

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

Using linear approximation, what is the estimate for 4.1\sqrt{4.1}?

2.0252.025

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

(1+x)n1+nx(1 + x)^n ≈ 1 + nx

Using Taylor series, what is the approximation for e0.1e^{0.1} near x=0x = 0?

1.1051.105

When does the binomial approximation (1+x)n1+nx(1 + x)^n ≈ 1 + nx work best?

When xx is small

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