What is the value of this limit?
lim (x^2+4/^2-3x+1)
x->4
A. 1
B. 4
C. 5
D -oo
E. oo
***x^2-3x+1
is this
lim (x^2 + 4)/(x^2 - 3x + 1)
x ---> 4
the first step in any limit is to actually sub in the approach value
in this case we get
lim(16+4)/(16 - 12 + 1)
= 20/5
= 4 , which is a real number, so we have no problem with this limit
the answer is 4 , all done!
To find the value of the limit, we can plug in the value of x that the limit is approaching and simplify the expression. In this case, the limit is approaching x = 4.
Let's substitute x = 4 into the expression:
lim (x^2 + 4) / (2 - 3x + 1) as x approaches 4
= (4^2 + 4) / (2 - 3(4) + 1)
= (16 + 4) / (2 - 12 + 1)
We simplify the denominator first:
= (20) / (-9)
= -20/9
Therefore, the value of the limit is -20/9.
So, none of the given options A, B, C, D, or E is the correct answer. The correct answer is -20/9.