How do you find the limit of #(2x-3)/(x+5)# as #x->3#?

Answer 1

#3/8#

#"evaluate using direct substitution"#

#lim_(xto3)(2x-3)/(x+5)=(6-3)/(3+5)=3/8#

Note that this works because the function is continuous at #x=3#. Note: #lim_(x->c)f(x)=f(c)# when the function is continuous at #c#

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Answer 2

Charles Anctil

To find the limit of (2x-3)/(x+5) as x approaches 3, we can substitute the value of 3 into the expression. This gives us (2(3)-3)/(3+5), which simplifies to (6-3)/(8). Further simplifying, we get 3/8. Therefore, the limit of (2x-3)/(x+5) as x approaches 3 is 3/8.

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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.

How do you find the limit of #(2x-3)/(x+5)# as #x-&gt;3#?

How do you find the limit of #(2x-3)/(x+5)# as #x->3#?