Calculus 3

How do we know that Integral test can be applied in testing infinite series whether converges or diverges

• Integral test can be applied to test the convergence or divergence of an infinite series if the series is negative
• Integral test can be applied to test the convergence or divergence of an infinite series if the series is not continuous
• Integral test can be applied to test the convergence or divergence of an infinite series if the series is increasing
• Integral test can be applied to test the convergence or divergence of an infinite series if the series is positive, continuous, and decreasing on a closed interval [1, ∞). If the integral of the function representing the series converges, then the series also converges. If the integral diverges, then the series also diverges.

What is the usual behavior of a harmonic series

• It converges
• It oscillates
• It diverges
• It remains constant

What is the alternating series test used for?

• To test the convergence or divergence of an infinite series with alternating signs

• To test the convergence or divergence of an infinite series with only positive terms

• To test the convergence or divergence of an infinite series with only negative terms

• To test the convergence or divergence of an infinite series with random terms

When can the ratio test be applied to determine the convergence of an infinite series?

• When the series has alternating signs

• When the series has only positive terms

• When the series has only negative terms

• When the series has terms that are eventually nonzero and follow a certain pattern

What is the purpose of the root test in analyzing infinite series?

• To determine if the series converges absolutely or conditionally

• To determine if the series has a finite number of terms

• To determine if the series has an infinite number of terms

• To determine if the series has a constant ratio between consecutive terms

• diverging

• diverge conditionally

• converge conditionally

• converging

• Converges
• Converges to 0
• Oscillates
• Diverges

The Limit comparison test states that the ratio of the terms of the two series is zero then both the series must converge. The statement is

• False

• True

• partially correct

• conditionally true

The Limit comparison test can be used to determine the convergence or divergence of a series when the terms of the series are positive

• partially correct

• False

• True

• conditionally true

The Limit comparison test can only be used to determine the convergence of a series, not its divergence

• False

• conditionally true

• partially true

• True