How do you determine the limit of # (1/(x^(2)(x+7)))# as x approaches #0#?

Answer 1

Scarlett Allison

#= oo#

#lim_(x to 0) 1/(x^(2)(x+7))#

#= lim_(x to 0) 1/(x^2) * 1/(x+7)#

limit of product is product of limits #= lim_(x to 0) 1/(x^2) *lim_(x to 0) 1/(x+7)#

#= lim_(x to 0) 1/(x^2) *lim_(x to 0) 1/(7)#

#= oo#

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Answer 2

Cameron Alexander

To determine the limit of (1/(x^(2)(x+7))) as x approaches 0, we can simplify the expression by factoring the denominator. Factoring x^2(x+7) gives us x^2 * (x+7). Since the numerator is 1, we can cancel out the x^2 term in the denominator. This leaves us with 1/(x+7).

Now, we can evaluate the limit as x approaches 0 by substituting 0 into the expression. Plugging in 0 for x gives us 1/(0+7), which simplifies to 1/7. Therefore, the limit of (1/(x^(2)(x+7))) as x approaches 0 is 1/7.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.