How do you find the limit of #(5x)/sqrt(x+2)# as #x->7#?

Answer 1

#lim_(x->7) (5x)/sqrt(x+2) =35/3#

#f(x)# is a rational function and as such it is continuous for every #x# in its domain. As the function is defined for #x=7# so, by definition of continuity, its limit equals its value:
#lim_(x->7) (5x)/sqrt(x+2) = [(5x)/sqrt(x+2)]_(x=7) = (5*7)/sqrt(7+2) =35/sqrt(9) =35/3#
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Answer 2

To find the limit of (5x)/sqrt(x+2) as x approaches 7, we can use direct substitution. Plugging in x=7 into the expression, we get (5*7)/sqrt(7+2), which simplifies to 35/sqrt(9). The square root of 9 is 3, so the expression becomes 35/3. Therefore, the limit of (5x)/sqrt(x+2) as x approaches 7 is 35/3.

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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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