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Answer :
The limit as x approaches -3 of 4(-3)³(x+3)² is 432.
The limit as x approaches -3 of 3x√(x² + 5) is -18√14.
For the first limit, we have the expression 4(-3)³(x+3)². Simplifying this expression, we get 4(-27)(x+3)², which further simplifies to -108(x+3)². When we evaluate the limit as x approaches -3, we substitute -3 into the expression, resulting in -108(-3+3)² = -108(0)² = 0. Therefore, the limit is 0.
For the second limit, we have the expression 3x√(x² + 5). As x approaches -3, we substitute -3 into the expression, giving us 3(-3)√((-3)² + 5). Simplifying further, we have -9√(9 + 5) = -9√14. Therefore, the limit is -9√14.
In summary, the limit as x approaches -3 of 4(-3)³(x+3)² is 432, and the limit as x approaches -3 of 3x√(x² + 5) is -18√14.
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