What is the limit of (sin x)/x as x tends to 0?

Rank by growth as x goes to infinity, slowest first. Which ordering is right?

• ln x, x, x squared, e^x
• x, ln x, x squared, e^x
• e^x, x squared, x, ln x
• ln x, e^x, x, x squared

When may you use the rule?

• On 0 over 0 or infinity over infinity quotients
• On any quotient of differentiable functions
• On any product that tends to zero

Applying the rule means differentiating the whole quotient with the quotient rule.

What is the limit of x squared/e^x as x tends to infinity?

e to the x grows faster than any fixed power of x.

Apply the rule twice to find the limit of (1 - cos x)/x squared as x tends to 0.

• 1
• 0
• 0.5
• 2

e^x grows faster than any fixed power x^k. True or false?

What is the limit of x to the 100 over e to the x as x tends to infinity?

• It diverges to infinity
• 100
• It tends to 0

What is the limit of x^100/e^x as x tends to infinity?

• it diverges to infinity
• 100
• 1
• it tends to 0