How do you find the limit #lim_(h->0)((4+h)^2-16)/h# ?

Answer 1
#lim_{h to 0}{(4+h)^2-16}/h=8#

Let us look at some details.

#lim_{h to 0}{(4+h)^2-16}/h#

by multiplying out the numerator,

#=lim_{h to 0}{16+8h+h^2-16}/h#
by cancelling out #16#'s,
#=lim_{h to 0}{8h+h^2}/h#
by factoring out #h# from the numerator,
#=lim_{h to 0}{h(8+h)}/h#
by cancelling out #h#'s,
#=lim_{h to 0}(8+h)=8+0=8#
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Answer 2

To find the limit of the given expression, we can simplify it algebraically.

Expanding the numerator, we have (4+h)^2 = 16 + 8h + h^2.

Subtracting 16 from the numerator, we get 8h + h^2.

Now, we divide the numerator by h, which gives us (8h + h^2)/h = 8 + h.

As h approaches 0, the limit of 8 + h is simply 8.

Therefore, the limit of ((4+h)^2-16)/h as h approaches 0 is 8.

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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.

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.

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.

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.

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