Chapter 1: Q. 11 (page 135)

Explain how the algebraic function $f (x) = {(\sqrt{x} + 1)}^{3}$ is a combination of identity, constant, and power functions. Why does this mean that we can calculate limits of this function at domain points by evaluation?

Short Answer

Expert verified

By the sum and composition rules for limits, and the fact that power and constant functions are continuous, we know that this functionf is continuous and thus we can calculate its limits at domain points by evaluation.

Step by step solution

Step 1. Given information

The given algebraic function $f (x) = {(\sqrt{x} + 1)}^{3}$

Step 2. The strategy is to explain that the above function is a combination of identity, constant and power functions.

To get this function we add the power function

\sqrt{x}

and the constant term 1 , and then compose the result with the power function

x^{3}

. Thus by the sum and composition rules for limits, and the fact that power and constant functions are continuous, we know that this function

f

is continuous and thus we can calculate its limits at domain points by evaluation.

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Explain how the algebraic function $f (x) = {(\sqrt{x} + 1)}^{3}$ is a combination of identity, constant, and power functions. Why does this mean that we can calculate limits of this function at domain points by evaluation?

Short Answer

Step by step solution

Step 1. Given information

Step 2. The strategy is to explain that the above function is a combination of identity, constant and power functions.

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Explain how the algebraic function f(x)=x+13 is a combination of identity, constant, and power functions. Why does this mean that we can calculate limits of this function at domain points by evaluation?

Short Answer

Step by step solution

Step 1. Given information

Step 2. The strategy is to explain that the above function is a combination of identity, constant and power functions.

One App. One Place for Learning.

Most popular questions from this chapter

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Explain how the algebraic function $f (x) = {(\sqrt{x} + 1)}^{3}$ is a combination of identity, constant, and power functions. Why does this mean that we can calculate limits of this function at domain points by evaluation?