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n. Given that (1+x) 1+ax - bx? + Find the values of a and b 2 1 + ax - -bx² + Find the values of a and b ... 3

n. Given that (1+x) 1+ax - bx? + Find the values of a and b 2 1 + ax - -bx² + Find the values of a and b ... 3

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Solve all Q13, 14 explaining detailly each step

7x 2. The first three terms in an expansion of (l+bx)(1- ax) as a series in ascending powers of x are 1 and x. Given that a > 0, find the values of a and b. 3. When x and higher powers of x are neglected, (4 + ax) + (4 + ax) = b + 3x+ cx². Find the values of the real constants a, b and c. state the range of values of x for which the expansion is ascending powers of x is valid. CX x+2 Given that g(x)=,x+ x* + 2x +2 and that f(x) g(x) expand f(x) as a series in ascending powers of %3D x up to and including the term x. Obtain also the range of values of x for which the complete expansion is valid. (NB. First show that x + 1 is a factor of g(x) and also express f(x) in partial fractions) 12 3/ Find the term independent of x in the expansion of (x +-) Expand (1 +x)as series of ascending powers of x as far as the term x". By putting x 1/3 obtain an approximation to V65 to 3 decimal places. 2 1/3 1--2x V. Given that f(x) = obtain the expansions of f(x) as a series of ascending powers of x up to and V 1+4x 7 including the term in x'. Verify that f) = 2V13 Hence, use your expansion to obtain to 2 decimal places an approximate value for v13. 8. Expand (2+3x) in ascending powers of x up to and including the term in x. State the range of values of x for which the expansion is valid. 10 3 O Find the coefficient of x in the binomial expansion of AGiven that gtx)= express g(x) in partial fractions. Hence, or eherwise, obtain the first (x-1)(x+1)' three terms in the expansion of g(x) in ascending powers of x. 4. Show that if x is so smail that x and higher powers can be neglected, then: = 1+x+xr? 2-3x 12 Given that: f(x) express f(x) as a series in ascending powers of x, up to and including (1-x)(2-x) the term in x, giving the range of values of x for which the expansion is valid. ro. Given that (1+x 1 ax 3. -bx² +.Find the values of a and b 3. 14, The first three terms in the expansion of who 1-x are 1, -2x and 4x? respectively. Determine the value 1+kx of k and state the range of values of x for which the expansion is valid.
Transcribed Image Text:7x 2. The first three terms in an expansion of (l+bx)(1- ax) as a series in ascending powers of x are 1 and x. Given that a > 0, find the values of a and b. 3. When x and higher powers of x are neglected, (4 + ax) + (4 + ax) = b + 3x+ cx². Find the values of the real constants a, b and c. state the range of values of x for which the expansion is ascending powers of x is valid. CX x+2 Given that g(x)=,x+ x* + 2x +2 and that f(x) g(x) expand f(x) as a series in ascending powers of %3D x up to and including the term x. Obtain also the range of values of x for which the complete expansion is valid. (NB. First show that x + 1 is a factor of g(x) and also express f(x) in partial fractions) 12 3/ Find the term independent of x in the expansion of (x +-) Expand (1 +x)as series of ascending powers of x as far as the term x". By putting x 1/3 obtain an approximation to V65 to 3 decimal places. 2 1/3 1--2x V. Given that f(x) = obtain the expansions of f(x) as a series of ascending powers of x up to and V 1+4x 7 including the term in x'. Verify that f) = 2V13 Hence, use your expansion to obtain to 2 decimal places an approximate value for v13. 8. Expand (2+3x) in ascending powers of x up to and including the term in x. State the range of values of x for which the expansion is valid. 10 3 O Find the coefficient of x in the binomial expansion of AGiven that gtx)= express g(x) in partial fractions. Hence, or eherwise, obtain the first (x-1)(x+1)' three terms in the expansion of g(x) in ascending powers of x. 4. Show that if x is so smail that x and higher powers can be neglected, then: = 1+x+xr? 2-3x 12 Given that: f(x) express f(x) as a series in ascending powers of x, up to and including (1-x)(2-x) the term in x, giving the range of values of x for which the expansion is valid. ro. Given that (1+x 1 ax 3. -bx² +.Find the values of a and b 3. 14, The first three terms in the expansion of who 1-x are 1, -2x and 4x? respectively. Determine the value 1+kx of k and state the range of values of x for which the expansion is valid.
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