Answer:
B. The limits Lim x-->7 (x²-9x+14)/x-7 and lim x--> 7 (x-2) equals the same number when evaluated using direct substitution. The limit of both functions is 5
Step-by-step explanation:
Find the complete question in the attachment.
Given the limit of the functions
Lim x-->7 (x²-9x+14)/x-7
To solve this, we will need to factorize the quadratic function at the numerator first.
x²-9x+14
= x²-2x-7x+14
= x(x-2)-7(x-2)
= (x-7)(x-2)
The expression therefore becomes:
= lim x-->7 (x-7)(x-2)/x-7
= lim x-->7 (x-2)
Now substitute the value of x into the simplified function
lim x-->7 (x-2) = 7-2
lim x-->7 (x-2) = 5
Hence Lim x-->7 (x²-9x+14)/x-7 = 5
From the calculation above, it can be seen that Lim x-->7 (x²-9x+14)/x-7 = lim x--> 7 (x-2) = 5
Hence the correct answer based on the explanation above is B.
The limits Lim x-->7 (x²-9x+14)/x-7 and lim x--> 7 (x-2) equals the same number when evaluated using direct substitution.
