Asked by Hai
Find numbers a and b such that:
lim (sqrt(ax+b)-9)/x =1
x->0
lim (sqrt(ax+b)-9)/x =1
x->0
Answers
Answered by
Steve
lim (√(ax+b)-9)/x
= lim a/(2√(ax+b))
so, since we afre clearly dealing with lim = 0/0, we need
√(ax+b) = 9
ax+b = 81
a/(2√(ax+b)) = 1
a = 2√(ax+b)
a^2 = 4(ax+b)
a^2 = 4*81
a = 18
so, b=81
lim (√(18x+81)-9)/x = 1
verify at
https://www.wolframalpha.com/input/?i=limit+%28x-%3E0%29+%28%E2%88%9A%2818x%2B81%29-9%29%2Fx
= lim a/(2√(ax+b))
so, since we afre clearly dealing with lim = 0/0, we need
√(ax+b) = 9
ax+b = 81
a/(2√(ax+b)) = 1
a = 2√(ax+b)
a^2 = 4(ax+b)
a^2 = 4*81
a = 18
so, b=81
lim (√(18x+81)-9)/x = 1
verify at
https://www.wolframalpha.com/input/?i=limit+%28x-%3E0%29+%28%E2%88%9A%2818x%2B81%29-9%29%2Fx
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