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# Calculus/Mathematics

Question
What is the limit of (x^2+3x-40)/2x-10 when x->5 (x ->5 is under the lim icon).

Thank you for time, John

Hi John,
Direct substitution results in the 0/0 form which is indeterminate, as you would have found. The next thing to try is simplification of the expression.
(x² + 3x - 40)/(2x - 10) = (x - 5)(x + 8) / 2(x - 5)
= (x + 8)/2
Therefore,
lim(x → 5) [(x² + 3x - 40)/(2x - 10)] = lim(x → 5) [(x + 8)/2]
= (5 + 8)/2
= 13/2

There is also a method, using calculus, which enables us to write the limit directly in this case as
lim(x → 5) [(x² + 3x - 40)/(2x - 10)] = lim(x → 5) [(2x + 3)/2]
= (10 + 3)/2
= 13/2

Regards

Calculus

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