Evaluate the following limit. lim_y rightarrow 3 y^2 + 2y - 15/Squareroot 18 - y

Question

Evaluate the following limit. lim_y rightarrow 3 y^2 + 2y - 15/Squareroot 18 - y^2 - y How should the given limit be evaluated? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Simplify the expression inside the limit to obtain lim_y rightarrow 3 (___ ). Use direct substitution. Use I'Hopital's Rule exactly once to rewrite the limit as lim_y rightarrow 3 (___ ). Use I'Hôpital's Rule more than once, rewrite the limit in its final form as lim_y rightarrow 3 (___ ). Evaluate the limit. lim_y rightarrow 3 y^2 + 2y - 15/Squareroot 18 - y^2 - y =___(Simplify your answer.)

Explanation / Answer

Given

lim y->3 [ y2 + 2y-15]/[sqrt(18-y2-y]

use direct subsituton

= [ 32 +2*3-15]/[sqrt(18-32-3]

= 0/sqrt(6)

= 0

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