Q3P Find the two-variable Maclaurin ... [FREE SOLUTION]

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Chapter 4: Q3P (page 192)

Find the two-variable Maclaurin series for the following functions.
$\frac{In (1 + x)}{1 + y}$

Short Answer

Expert verified

$f (x, y) = x - \frac{x^{2}}{2} - xy + \frac{x^{3}}{3} + \frac{x^{2} y}{2} + {xy}^{2} . . . . . .$

Step by step solution

Explanation of solution

The equation is provided $\frac{In (1 + x)}{1 + y}$ and to find the two variable Maclaurin for the following function.

McLaren Series:

If the values of the function's consecutive derivatives at zero are known, a Maclaurin series can be used to approximate a function f(x) with input values close to zero. In many practical applications, it is equivalent to the function it represents.

Calculation

The following equation is provided:

$f (x, y) = \frac{In (1 + x)}{1 + y} - - - - - - (1)$

Since, $(1 + x) = x - \frac{x^{2}}{2} + \frac{x^{3}}{3} - \frac{x^{4}}{4} + . . . - - - - (2)$

And, ${(1 + y)}^{- 1} = 1 - y + y^{2} - y^{3} + y^{4} - y^{5} + . . . - - - - - (3)$

Substitute (2) and (3) in (1),

$f (x, y) = I n (1 + x) {(1 + y)}^{- 1} = x - \frac{x^{2}}{2} - x y + \frac{x^{3}}{3} + \frac{x^{2} y}{2} + x y^{2} . . . . . . = x - \frac{x^{2}}{2} - x y + \frac{x^{3}}{3} + \frac{x^{2} y}{2} + x y^{2} . . . . . .$

Hence, $f (x, y) = x - \frac{x^{2}}{2} - x y + \frac{x^{3}}{3} + \frac{x^{2} y}{2} + x y^{2} . . . . . . .$

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91影视

Find the two-variable Maclaurin series for the following functions.
$\frac{In (1 + x)}{1 + y}$

Short Answer

Step by step solution

Explanation of solution

Calculation

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91影视

Find the two-variable Maclaurin series for the following functions.In(1+x)1+y

Short Answer

Step by step solution

Explanation of solution

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Thermodynamics

Kinematics Physics

Atoms and Radioactivity

Electric Charge Field and Potential

Further Mechanics and Thermal Physics

Fields in Physics

Study anywhere. Anytime. Across all devices.

Find the two-variable Maclaurin series for the following functions.
$\frac{In (1 + x)}{1 + y}$