Question

Find the number a such that the limit exists: lim_(x → a) (2x² - ax + 6).

a) a = 4
b) a = 2
c) a = 3
d) a = 6

Answer 1

The limit of the polynomial function exists for any value of 'a' as polynomial functions are continuous everywhere. Therefore, any option provided is a valid answer.

Step-by-step explanation:

The question requires finding the value of a such that the limit of the function
`f(x) = 2x² - ax + 6` exists as x approaches a. Since this is a polynomial function, we know that polynomial functions are continuous for all real numbers. Therefore, the limit as x approaches a will exist for any real value of a.

The limit of a polynomial function is simply the function value at the point a, which is to say that for
`f(x) = 2x² - ax + 6`, the limit as x approaches a is
`f(a) = 2a² - a² + 6 = a² + 6`. Therefore the limit exists for any real value of a and all options given are valid.