Understanding Limits in Calculus

The video tutorial explores the concept of limits in calculus, focusing on the limits of functions f(x) and h(x) as x approaches 0. It explains how to determine these limits using graphical depictions and limit properties. The tutorial also examines the limit of h(x) over g(x), highlighting the issue of division by zero and the non-existence of the limit in such cases.

What is the limit of the product of two functions as x approaches 0?

• The quotient of the limits of the two functions

• The difference of the limits of the two functions

• The product of the limits of the two functions

• The sum of the limits of the two functions

What value does f(x) approach from both sides as x approaches 0?

• 1

• -1

• 2

• 0

Why is the limit of f(x) as x approaches 0 equal to -1?

• Because the function is defined at x=0

• Because the function approaches -1 from both sides

• Because the function is undefined at x=0

• Because the function is continuous

What is the value of h(x) at x=0?

• 0

• 1

• 2

• 3

Why is the limit of h(x) as x approaches 0 equal to its value at x=0?

• Because h(x) is a constant function

• Because h(x) is discontinuous

• Because h(x) is undefined at x=0

• Because h(x) is continuous

What happens when you try to divide 4 by 0 in the context of limits?

• The limit exists and is 4

• The limit exists and is 0

• The limit is infinite

• The limit does not exist

What is the limit of h(x) as x approaches 0?

• 4

• 2

• 1

• 0

What is the limit of g(x) as x approaches 0?

• 4

• 2

• 1

• 0

Why does the limit of h(x)/g(x) not exist as x approaches 0?

• Because both h(x) and g(x) are zero

• Because you cannot divide by zero

• Because g(x) is undefined

• Because h(x) is undefined

What would you observe if you plotted h(x)/g(x) as x approaches 0?

• A graph with a hole at x=0

• A graph with a vertical asymptote

• A graph with a horizontal asymptote

• A continuous graph