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What is this limit? Without using lopital rule

What is this limit? Without using lopital rule-example-1
User Yong Wang
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1 Answer

6 votes

Answer:

60.

Explanation:

(x^2 - 25) / (√(x + 4) - 3).

We rationalise the expression by multiplying top and bottom of the fraction by the complement of the denominator.

That is by (√(x + 4) + 3):

(x^2 - 25)(√(x + 4) + 3)

= ------------------------------------

(√(x + 4) - 3)(√(x + 4) + 3)

= (x + 5)(x - 5)(√(x + 4) + 3)

----------------------------------

(x - 5)

= (x + 5)(√(x + 4) + 3).

The limit as this---> 5

is (5 + 5)(√(5 + 4) + 3)

= 10 * 6

= 60.

User Siddharth Trikha
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4.1k points