find the limit:
Lim (49x^2-25)/(7x-5)
x->5/7
since 79x^2 - 25 = (7x-5)(7x+5)
f(x) = 7x+5 for x ≠ 5/7
so, the limit is 7(5/7) + 5 = 10
thank u
To find the limit of the given expression as x approaches 5/7, we can directly substitute the value of x into the expression.
Let's substitute x = 5/7 into the expression (49x^2 - 25)/(7x - 5):
Lim (49(5/7)^2 - 25)/(7(5/7) - 5)
Simplifying the calculation:
Lim (49(25/49) - 25)/(35/7 - 5)
Lim (25 - 25)/(5 - 5)
Lim 0/0
We have obtained an indeterminate form of 0/0, which means we cannot determine the limit by direct substitution.
To resolve this, we can factorize the numerator and denominator to simplify the expression. Factoring the numerator:
49x^2 - 25 = (7x - 5)(7x + 5)
Now, let's rewrite the expression:
Lim (7x + 5)(7x - 5)/(7x - 5)
Now, we can cancel out the common factor of (7x - 5) from the numerator and denominator:
Lim (7x + 5)
Now, we can substitute x = 5/7 into the simplified expression:
Lim (7(5/7) + 5)
Simplifying further:
Lim (5 + 5)
Lim 10
Therefore, the limit of the expression (49x^2 - 25)/(7x - 5) as x approaches 5/7 is equal to 10.