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Answer :
Final answer:
To evaluate the limit of the expression, we use conjugate multiplication to simplify the expression and find the value. The value of the limit as x approaches 4 is 4 - √5.
Explanation:
To evaluate the limit of the given expression, we need to substitute the value of x into the expression and simplify. Since the expression has a discontinuity at x = 4, the value of the expression at x = 4 cannot be obtained by direct substitution. We can use a technique called conjugate multiplication to simplify the expression and find the limit. The conjugate of the denominator is (x - 4), so by multiplying both the numerator and denominator by the conjugate, we can eliminate the square root and simplify the expression to -√5 + x.
Now, substitute x = 4 into the simplified expression:
-√5 + 4 = 4 - √5
Therefore, the value of the limit as x approaches 4 is 4 - √5.
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