Question

Explain the meaning of each of the following. (a) lim x → −3 f(x) = [infinity] The values of f(x) can be made arbitrarily close to 0 by taking x sufficiently close to (but not equal to) −3. The values of f(x) can be made arbitrarily large by taking x sufficiently close to (but not equal to) −3.

Answer 1

Answer:

The right answer is option 3.

lim x → −3 f(x) = [infinity] means the values of f(x) can be made arbitrarily large by taking x sufficiently close to (but not equal to) −3.

Step-by-step explanation:

The limit of a function is a fundamental concept concerning the behavior of that function near a particular input.

A function f assigns an output f(x) to every input x. We say the function has a limit L at an input a: this means f(x) gets closer and closer to L as x moves closer and closer to a. More specifically, when f is applied to any input sufficiently close to a, the output value is forced arbitrarily close to L.

That is,

lim x → a f(x) = L

Hope this helps!