Find the limit (x^2+x-6)/(x+3) when x approach -3.
- print Print
- list Cite
Expert Answers
calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
limit (x^2+x-6)/(x+3) when x approaches -3
first we need to find the value of the function when x=-3
then, lim...
(The entire section contains 70 words.)
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Related Questions
- Find the limit: limx^sinx as x approaches to 0+.
- 1 Educator Answer
- The limit of `[sqrt(9x^2+x)-3x]` as x approaches infinity
- 1 Educator Answer
- Find limits: 1.) lim x-->2 (8-x^3)/(x^2-5x+6) 2.) lim x-->-1 (x^2-5x+6)/(x^2-3x+2) 3.) lim...
- 2 Educator Answers
- Find the inverse function of f(x)=x^3+2?
- 1 Educator Answer
- Calculate the limit of the function, if it exists? limit (x^2+x-6)/(x-2), x->2
- 1 Educator Answer
For evaluating the limit, we'll choose the dividing out technique.
We'll apply the direct substitution, by substituting the unknown x, by the value -3 and we'll see that it fails, because both, numerator and denominator, are cancelling for x=-3. That means x=-3 is a root for both, that means that (x+3) is a common factor for both.
We'll write the numerator using the formula:
x^2+x-6=(x-x1)(x-x2), where x1, x2 are the roots and x1=-3
x^2+x-6=(x+3)(x-x2)
We also know that x1+x2 = -1, -3+x2=-1
and x1*x2=-6, (-3)*x2=-6
x2=2
Now, we'll evaluate the limit:
lim (x^2+x-6)/(x+3) = lim (x+3)(x-2)/(x+3)
Now, we can divide out like factor:
lim (x^2+x-6)/(x+3) = lim (x-2)
We can apply the replacement theorem and we'll get:
lim (x-2) = -3-2 = -5
So, lim (x^2+x-6)/(x+3) = -5.
To find the lt (x^2+x-6)/(x+3) as xapproaches -3.
Solution:
We see that f(x) = (x^2+x-6)/(x+3) goes for 0/0 form at x=-3.
So we try numerator. :
f(x) = (x+3)(x-2/(x+3) = x-2.
Therefore, lt x--> -3 f(x) = lt x--> 3 of (x-2 ) = (-3-2) = -5.
Student Answers