Maclaurin Series Concepts and Applications

The video tutorial explains how to find the Maclaurin series for the function f(x) = 5cos(3x^2). It begins by introducing the concept of a Maclaurin series and the formula used to derive it. Instead of calculating derivatives manually, the tutorial uses the known Maclaurin series for cosine to simplify the process. By substituting 3x^2 for x and multiplying by 5, the series is expanded to find the coefficients c_0 through c_8. The tutorial concludes by expressing the series in summation notation, providing a clear and efficient method for finding the Maclaurin series of the given function.

What is the function for which we are finding the Maclaurin series?

• f(x) = 5cos(x^2)

• f(x) = 3cos(5x^2)

• f(x) = 5cos(3x^2)

• f(x) = 5sin(3x^2)

What is the center of the Maclaurin series?

• c = 5

• c = 0

• c = 3

• c = 1

Which rule is applied to find the first derivative in the Maclaurin series?

• Chain rule

• Product rule

• Quotient rule

• Power rule

What is the known series used to build the Maclaurin series for the given function?

• Cosine series

• Sine series

• Logarithmic series

• Exponential series

What substitution is made to find the Maclaurin series for 5cos(3x^2)?

• Substitute 3x^2 for x

• Substitute 3x for x

• Substitute x^2 for x

• Substitute 5x^2 for x

What is the coefficient c0 in the series?

• 0

• 5

• 135/8

• 45/2

What is the coefficient c4 in the series?

• 135/8

• -45/2

• 5

• 0

What is the coefficient c8 in the series?

• 5

• -45/2

• 135/8

• 0

How is the final Maclaurin series expressed?

• Using integral notation

• Using differential notation

• Using summation notation

• Using product notation

What is the factor brought into the summation in the final expression?

• 2n

• 5

• x

• 3