Limit of a Sequence

Which of the following sequences has a limit that is a fixed real number ?

• 2, 4, 8, 16, ...

• -3, 6, -12, 24, ...

• 0.6, 0.06, 0.006, 0.0006,...

• 10, 9, 8, 7, 6, ...

What is the limit of the sequence \frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{16},\frac{1}{32},......\ ?

• o

• 1

• 1.5

• 1.9

• 1.99

• 2

The limit of the sequence whose nth term is above, is... (ie: as n gets bigger and bigger, the fraction approaches...)

• 0

• 1

• 2

• infinity

Determine whether the sequence converges or diverges. If it converges, give the limit.

• Diverges

• Converges to 1

• Converges to 0

​

• converges to -5

• diverges

• converges to 0

• converges to 5/3

• converges to 5

• converges to 4/3

• converges to 4

• converges to -4

• Converges to 0

• Converges to 1

• Converges to 5

• Diverges

• Converges to 0

• Converges to 2

• Converges to 5

• Diverges

It is the value that function approaches as the independent variable of the function approaches a given value.

• Limit

• Derivative

• Constant

• Tangent

For a limit to exist, the left and the right hand limits must be equal.

• True

• False