To find the limit of the given expression as x approaches 7, let's first simplify the expression:
The given expression is:lim (x→7) √x - 3 - 2/(x - 7)
To simplify, let's first combine the terms in the numerator:lim (x→7) √x - 3(x - 7)/(x - 7)
Now, simplify further:lim (x→7) √x - 3x + 21)/(x - 7)
Since we have a square root function involved, let's rationalize the numerator by multiplying both the numerator and the denominator by the conjugate of the numerator:lim (x→7) (√x - 3x + 21)(√x + 3x + 21)/(x - 7)(√x + 3x + 21)
Simplifying, we get:lim (x→7) (√x)^2 - (3x)^2 + 21^2)/(x - 7)√x + 3x + 21
lim (x→7) (x - 9)/√x + 3x + 21
Now, plug in x = 7 to find the limit:(7 - 9)/√7 + 3(7) + 21(-2)/√7 + 21 + 21-2/√7 + 42
Therefore, the limit as x approaches 7 of the given expression is -2/√7 + 42.
To find the limit of the given expression as x approaches 7, let's first simplify the expression:
The given expression is:
lim (x→7) √x - 3 - 2/(x - 7)
To simplify, let's first combine the terms in the numerator:
lim (x→7) √x - 3(x - 7)/(x - 7)
Now, simplify further:
lim (x→7) √x - 3x + 21)/(x - 7)
Since we have a square root function involved, let's rationalize the numerator by multiplying both the numerator and the denominator by the conjugate of the numerator:
lim (x→7) (√x - 3x + 21)(√x + 3x + 21)/(x - 7)(√x + 3x + 21)
Simplifying, we get:
lim (x→7) (√x)^2 - (3x)^2 + 21^2)/(x - 7)√x + 3x + 21
lim (x→7) (x - 9)/√x + 3x + 21
Now, plug in x = 7 to find the limit:
(7 - 9)/√7 + 3(7) + 21
(-2)/√7 + 21 + 21
-2/√7 + 42
Therefore, the limit as x approaches 7 of the given expression is -2/√7 + 42.