Question

Consider the function f(x)={x²-3 x+2}{x⁴ -4 x²

(a) Find lim _{x--->-2} f(x)
(b) Find lim _{x-->0} f(x)

Answer 1

To find the limits of the given function, we substitute the values into the function and simplify the expressions.

Step-by-step explanation:

To find the limit of a function, we substitute the given value into the function and see what value it approaches as the function gets closer to that value.

(a) To find limx → -2 f(x), we substitute -2 into the function f(x) and simplify:

f(-2) = (-2)² - 3(-2) + 2 = 4 + 6 + 2 = 12. Therefore, limx → -2 f(x) is equal to 12.

(b) To find limx → 0 f(x), we substitute 0 into the function f(x) and simplify:

f(0) = (0)² - 3(0) + 2 = 0 + 0 + 2 = 2. Therefore, limx → 0 f(x) is equal to 2.