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Evaluate the limit of

Evaluate the limit of-example-1
User Jvanrhyn
by
8.7k points

1 Answer

3 votes

Answer:

Option a is correct --
(9)/(2)

Explanation:

If we put infinity directly into the expression we get ∞ + ∞ expression. In order to circumvent it we divide both numerator and denominator with the greatest exponent.


\lim_(x \to \infty) (9n^(3)+5n-2)/(2n^(3))

Divide each term by n³


=\lim_(x \to \infty) ((9n^(3))/(n^(3))+(5n)/(n^(3)) -(2)/(n^(3)))/((2n^(3))/(n^(3)) )


=\lim_(x \to \infty)(9(1)+(5)/(n^(2))-(2)/(n^(3)))/(2(1)) } \\=\lim_(x \to \infty)(9+(5)/(n^(2))-(2)/(n^(3)))/(2)} \\\\by putting n = infinity (5)/(n^(2)) becomes 0 and(2)/(n^(3)) becomes 0 \\=(9+0-0)/(2) \\=(9)/(2)



User Wcolen
by
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