Solve all Q13, 14 explaining detailly each step 7x2.The first three terms in an expansion of (l+bx)(1- ax) as a series in ascending powers of x are 1and 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 thevalues of the real constants a, b and c. state the range of values of x for which the expansion isascending powers of x is valid.CXx+2Given that g(x)=,x+ x* + 2x +2 and that f(x)g(x)expand f(x) as a series in ascending powers of%3Dx up to and including the term x. Obtain also the range of values of x for which the completeexpansion is valid. (NB. First show that x + 1 is a factor of g(x) and also express f(x) in partialfractions)123/ 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 obtainan approximation to V65 to 3 decimal places.2 1/31--2xV. Given that f(x) =obtain the expansions of f(x) as a series of ascending powers of x up to andV 1+4x7including the term in x'. Verify that f) =2V13Hence, 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 ofvalues of x for which the expansion is valid.103O Find the coefficient of x in the binomial expansion ofAGiven 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?2-3x12 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 1ax3.-bx² +.Find the values of a and b3.14, The first three terms in the expansion ofwho1-xare 1, -2x and 4x? respectively. Determine the value1+kxof k and state the range of values of x for which the expansion is valid.

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Solve all Q13, 14 explaining detailly each step 7x2.The first three terms in an expansion of (l+bx)(1- ax) as a series in ascending powers of x are 1and 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 thevalues of the real constants a, b and c. state the range of values of x for which the expansion isascending powers of x is valid.CXx+2Given that g(x)=,x+ x* + 2x +2 and that f(x)g(x)expand f(x) as a series in ascending powers of%3Dx up to and including the term x. Obtain also the range of values of x for which the completeexpansion is valid. (NB. First show that x + 1 is a factor of g(x) and also express f(x) in partialfractions)123/ 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&#34;. By putting x 1/3 obtainan approximation to V65 to 3 decimal places.2 1/31--2xV. Given that f(x) =obtain the expansions of f(x) as a series of ascending powers of x up to andV 1+4x7including the term in x'. Verify that f) =2V13Hence, 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 ofvalues of x for which the expansion is valid.103O Find the coefficient of x in the binomial expansion ofAGiven 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?2-3x12 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 1ax3.-bx² +.Find the values of a and b3.14, The first three terms in the expansion ofwho1-xare 1, -2x and 4x? respectively. Determine the value1+kxof k and state the range of values of x for which the expansion is valid.

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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