Numerical Methods

The necessary condition for the McLaurin expansion to be true for function f(x) is __________

• f(x) should be continuous

• f(x) should be differentiable

• f(x) should exists at every point

• f(x) should be continuous and differentiable

The value of f(1) can be deduced using Taylor series.

• True

• False

Let τ_a(f(x)) denote the Taylor series of the polynomial f(x) centered at a. Which of the following exactly happens after the Taylor series is formed?

• τ_a(f(x)) = f(x)

• The Taylor series has the effect of scaling GRAPH OF f(x)

• The Taylor series transforms the origin

• Scaled up graph obtained by factor of a

A function f(x) which is continuous and differentiable over the real domain exists such that f⁽ⁿ⁾ (x) = [f^{(n + 1)} (x)]², f(0) = a and f⁽¹⁾(0) = 1.

• True

• False

Find the value of √10

• 3.1633

• 3.1623

• 3.1632

• 3.1645

Expand f(x) = ¹⁄_x about x = 1.

• 1 – (x-1) + (x-1)² – (x-1)³ + ….

• 1 + (x-1) + (x-1)² + (x-1)³ + ….

• 1 + (x-1) – (x-1)² + (x-1)³ + ….

• 1 – (x+1) + (x+1)² – (x+1)³ + ….

An infinite series that can be thought of as a polynomial with an infinite number of terms, such as 1 + x + x2 + x3 +⋯…

• Taylor Series

• Power Series

• Numerical Series

• Maclaurin Series

Type of series expansion in which all terms are nonnegative integer powers of the variable.

• Taylor Series

• Power Series

• Numerical Series

• Maclaurin Series

A function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point.

• Taylor Series

• Power Series

• Numerical Series

• Maclaurin Series

To find the value of sin(9) the Taylor Series expansion should be expanded with center as

• 9

• 8

• 7

• some delta with small interval around 9