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How do you find the limit #lim_(x->-4)(x^2+5x+4)/(x^2+3x-4)# ?

Answer 1

Cameron Alexander

#=3/5#

Explanation,

Using Finding Limits Algebraically,

#=lim_(x->-4)(x^2+5x+4)/(x^2+3x-4)# , if we plug #x=-4#, we get #0/0# form

#=lim_(x->-4)(x^2+4x+x+4)/(x^2+4x-x-4)#

#=lim_(x->-4)(x(x+4)+1(x+4))/(x(x+4)-1(x+4))#

#=lim_(x->-4)((x+4)(x+1))/((x+4)(x-1))#

#=lim_(x->-4)((x+1))/((x-1))#

#=(-3)/-5#

#=3/5#

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Answer 2

Scarlett Allison

To find the limit of the given expression, we can directly substitute the value of x into the expression and evaluate it. However, if the expression is undefined at that point, we need to use algebraic manipulation to simplify it before substituting the value. In this case, let's simplify the expression first:

(x^2 + 5x + 4) / (x^2 + 3x - 4)

Factoring the numerator and denominator, we get:

[(x + 4)(x + 1)] / [(x - 1)(x + 4)]

Since (x + 4) appears in both the numerator and denominator, we can cancel it out:

(x + 1) / (x - 1)

Now, we can substitute the value of x into the simplified expression:

lim_(x->-4) [(x + 1) / (x - 1)]

Plugging in x = -4, we get:

(-4 + 1) / (-4 - 1) = -3 / -5 = 3/5

Therefore, the limit of the given expression as x approaches -4 is 3/5.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you find the limit #lim_(x-&gt;-4)(x^2+5x+4)/(x^2+3x-4)# ?

How do you find the limit #lim_(x->-4)(x^2+5x+4)/(x^2+3x-4)# ?