evaluate lim x aproches -1
x^2+6x+5/x^2-3x-4
lim (x^2 + 6x + 5)/(x^2 - 3x - 4) as x-> -1
Not that we can factor both numerator & denominator,
lim (x+5)(x+1) / (x-4)(x+1)
We can thus cancel the x+1, leaving
lim (x + 5)/(x - 4) as x-> -1
Substituting x = -1,
= (-1 + 5) / (-1 - 4)
= 4 / -5
= -4/5
Hope this helps~ :3
To evaluate the limit of a function as x approaches a specific value, you can begin by direct substitution of the given value in place of x. However, if substituting the value directly results in an undefined expression (such as division by zero), further steps need to be taken.
In this case, as x approaches -1, we encounter a denominator of 0. Therefore, we need to perform algebraic manipulations to simplify the expression and determine the limit.
Let's factor the numerator and denominator separately:
Numerator:
x^2 + 6x + 5 = (x + 1)(x + 5)
Denominator:
x^2 - 3x - 4 = (x - 4)(x + 1)
Now, we can simplify the expression:
[(x + 1)(x + 5)] / [(x - 4)(x + 1)]
Since both the numerator and denominator have (x + 1) as a factor, we can cancel it out:
(x + 5) / (x - 4)
Now, we can substitute -1 directly into the simplified expression:
(-1 + 5) / (-1 - 4)
= 4 / -5
= -0.8
Therefore, the limit of the given function as x approaches -1 is -0.8.