Find limit as x approaches 1 5/(x-1)^2
A. 0
B. Negative infinity
C. 5/4
D. Infinity
E. None of these
what does x approach?
infinity, (x-1)^2 goes towards a tiny positive number.
To find the limit as x approaches 1 of the function 5/(x-1)^2, we can use the concept of limits.
We begin by substituting x = 1 into the expression and see what happens.
When x approaches 1, the expression (x-1)^2 becomes (1-1)^2 which equals 0. Since we cannot divide by zero, we have an indeterminate form.
To determine the limit, we can simplify the expression by factoring out a common term of (x-1)^2 in the numerator:
5/(x-1)^2 = 5/((x-1)(x-1))
Now, we can cancel out the common factor (x-1) in the numerator and denominator:
= 5/(x-1)
By evaluating the expression at x = 1, we get:
5/(1-1) = 5/0, which is undefined.
Thus, the given limit does not exist.
The correct answer is E. None of these.