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6 Without expanding, simplify: a 1 + 3(x – 1) + 3(x – 1)² + (x – 1)³ b 1- 6(x + 1) + 15(x + 1)² – 20(x + 1)³ + 15 (x + 1)4 – 6(x + 1)’ + (x + 1)" |

6 Without expanding, simplify: a 1 + 3(x – 1) + 3(x – 1)² + (x – 1)³ b 1- 6(x + 1) + 15(x + 1)² – 20(x + 1)³ + 15 (x + 1)4 – 6(x + 1)’ + (x + 1)" |

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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twice the sum of the coefficients in the first expansion. 5 Expand (1 + x)' and (1 + x)1º, and show that the sum of the coefficients in the second expansion i= ii find the term in x-2. DEVELOPME 6 Without expanding, simplify: a 1 + 3(x – 1) + 3(x – 1)² + (x – 1)³ b 1- 6(x + 1) + 15(x + 1)² – 20(x + 1)³ + 15 (x + 1)* – 6(x + 1)' + (x + 1)" 7 Find the coefficient of x* in the expansion of (1 x) + (1 – x) + (1 – x)°. 8 Find integers a and b such that: 3 a (1 + V3) = a + bV3 b (1- v5) = a + bV5 9 Verify by direct expansion, and by taking out the common factor, that: b (1 + x)7 - (1 + x)° = x(1 + x) 3. %3D a (1 + x)4 - (1 + x)³ = x(1 + x) %3D 10 Do not use a calculator in this question. a Expand the first few terms of (1 + x)°, hence evaluate 1.003° to five decimal places O Similarly, expand (1 - 4x), and hence evaluate 0.96° to five decimal places.
Transcribed Image Text:twice the sum of the coefficients in the first expansion. 5 Expand (1 + x)' and (1 + x)1º, and show that the sum of the coefficients in the second expansion i= ii find the term in x-2. DEVELOPME 6 Without expanding, simplify: a 1 + 3(x – 1) + 3(x – 1)² + (x – 1)³ b 1- 6(x + 1) + 15(x + 1)² – 20(x + 1)³ + 15 (x + 1)* – 6(x + 1)' + (x + 1)" 7 Find the coefficient of x* in the expansion of (1 x) + (1 – x) + (1 – x)°. 8 Find integers a and b such that: 3 a (1 + V3) = a + bV3 b (1- v5) = a + bV5 9 Verify by direct expansion, and by taking out the common factor, that: b (1 + x)7 - (1 + x)° = x(1 + x) 3. %3D a (1 + x)4 - (1 + x)³ = x(1 + x) %3D 10 Do not use a calculator in this question. a Expand the first few terms of (1 + x)°, hence evaluate 1.003° to five decimal places O Similarly, expand (1 - 4x), and hence evaluate 0.96° to five decimal places.
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