Understanding Limits and Infinity

The video tutorial explains the concept of limits, focusing on how values approach zero from both negative and positive directions. It uses graphical representations to illustrate these concepts, highlighting the behavior of functions as they approach infinity or negative infinity. The tutorial also covers the idea of undefined limits and explores the specific case of the limit of 1/x squared, emphasizing the symmetry and positive values involved.

What happens to the value of f(x) = 1/x as x approaches zero from the negative side?

• It approaches negative infinity

• It approaches positive infinity

• It approaches zero

• It remains constant

When x approaches zero from the positive side in the function f(x) = 1/x, what is the behavior of the function?

• It approaches positive infinity

• It approaches negative infinity

• It remains constant

• It approaches zero

Why is the limit of f(x) = 1/x undefined as x approaches zero?

• Because it approaches the same value from both sides

• Because it approaches different values from each side

• Because it approaches zero

• Because it remains constant

What does the function f(x) = 1/x approach as x becomes very large in the negative direction?

• Negative infinity

• A constant value

• Positive infinity

• Zero

In the context of limits, what does it mean for a function to asymptote?

• It remains undefined

• It approaches a constant value

• It approaches zero

• It approaches infinity

In the function f(x) = 1/x^2, what happens as x approaches zero from either side?

• It remains constant

• It approaches negative infinity

• It approaches positive infinity

• It approaches zero

What is the significance of squaring x in the function f(x) = 1/x^2?

• It makes the function approach negative infinity

• It ensures the function is always positive

• It makes the function approach zero

• It makes the function remain constant

How does the graph of f(x) = 1/x^2 behave as x approaches zero?

• It remains constant

• It approaches negative infinity

• It approaches positive infinity symmetrically

• It approaches zero

What is the overall limit of f(x) = 1/x^2 as x approaches zero?

• Zero

• Negative infinity

• Positive infinity

• Undefined

Why is the concept of infinity exciting in the context of limits?

• Because it is always zero

• Because it is always negative

• Because it is undefined

• Because it is a legitimate answer