InterviewSolution
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InterviewSolution
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Find the values of a and b in order that `lim_(xto0) (x(1+acosx)-bsinx)/(x^(3))=1.` |
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Answer» Correct Answer - `a=(-5)/(2),b=(-3)/(2)` `underset(xto0)lim(x(1+acosx)-bsinx)/(x^(3))=1" "`(0/0 form) `impliesunderset(xto0)lim(x+axcosx-bsinx)/(x^(3))=1` `impliesunderset(xto0)lim(x+ax(1-(x^(2))/(2!)+(x^(4))/(4!)+...)-b(x-(x^(3))/(3!)+(x^(5))/(5!)+...))/(x^(3))=1` `impliesunderset(xto0)lim((1+a-b)x+(-(a)/(2)+(b)/(6))x^(3))/(x^(3))=1` `implies1+a-b=0" "(1)` and `-a/2+b/6=1" "(2)` Solving equations (1) and (2), we get `a=-(5)/(2),b=-(3)/(2).` |
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