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How do you find the limit of #(5x^2-8x-13)/(x^2-5)# as x approaches 3?

Answer 1

Use the properties of limits.

#lim_(xrarr3)(x^2-5)=lim_(xrarr3)x^2-lim_(xrarr3)5# (Subtraction property) #=(lim_(xrarr3)x)^2-lim_(xrarr3)5# (Power property) #=3^2-5# (Limits of Identity and constant functions) #=9-5=4# (Arithmetic)

Because the limit of the denominator is not #0#, we can use the quotient property for limits.

By steps similar to those above, we can show that #lim_(xrarr3)(5x^2-8x-13)=5(3)^2-8(3)-13=45-37=8#.

And, therefore #lim_(xrarr3)(5x^2-8x-13)/(x^2-5)=8/4=2#.

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Answer 2

William Abdalla

To find the limit of (5x^2-8x-13)/(x^2-5) as x approaches 3, we can substitute 3 into the expression and simplify. By substituting 3 for x, we get (5(3)^2-8(3)-13)/(3^2-5). Simplifying further, we have (45-24-13)/(9-5), which becomes 8/4. Therefore, the limit is equal to 2.

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Answer 3

William Abdalla

To find the limit of (5x^2 - 8x - 13) / (x^2 - 5) as x approaches 3, first substitute 3 for x in the expression. Then simplify the expression to find the limit.

(5(3)^2 - 8(3) - 13) / ((3)^2 - 5)

= (45 - 24 - 13) / (9 - 5)

= (8) / (4)

= 2

Therefore, the limit of the expression as x approaches 3 is 2.

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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.