Ali D.
asked • 03/30/21If a and b are constants and lim x→0 (a sin(5x)−5b xcos(x)) / (5tan(2x)+2sin(5x)) = 6, then a−b=
If a and b are constants and lim x→0 (a sin(5x)−5b xcos(x)) / (5tan(2x)+2sin(5x)) = 6, then a−b=
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1 Expert Answer
Yefim S. answered • 03/30/21
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lim x →0 (asin(5x) - 5bxcos(x))/(5tan(2x) + 2sin(5x)) = lim x→0 (5acos(5x) - 5bcos(x) + 5bxsin(x))/(10sec2(2x) + 10cos(5x)) = (5a - 5b)/20 = (a - b)/4 = 6; so, a - b = 24.
To get this limit we used L'opital's rule.
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Paul M.
03/30/21