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NeTakaya
3 years ago
11

1. Kalena was asked to prove ifx(x - 1)(x + 1) = x3 - X represents a polynomial identity. She

Mathematics
1 answer:
Verdich [7]3 years ago
6 0

Answer:

C. Kalena made a mistake in Step 3. The justification should state: -x²

+ x²

Step-by-step explanation:

Given the function x(x - 1)(x + 1) = x3 - X

To justify kelena proof

We will need to show if the two equations are equal.

Starting from the RHS with function x³-x

First we will factor out the common factor which is 'x' to have;

x(x²-1)

Factorising x²-1 using the difference of two square will give;

x(x+1)(x-1)

Note that for two real number a and b, the expansion of a²-b² using difference vof two square will give;

a²-b² = (a+b)(a-b) hence;

Factorising x²-1 using the difference of two square will give;

x(x+1)(x-1)

Factorising x(x+1) gives x²+x, therefore

x(x+1)(x-1) = (x²+x)(x-1)

(x²+x)(x-1) = x³-x²+x²-x

The function x³-x²+x²-x gotten shows that kelena made a mistake in step 3, the justification should be -x²+x² not -x-x²

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Answer:

The values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001 is 0 < x < 0.3936.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore provided before answering the question as follows:

Determine the values of x for which the function can be replaced by the Taylor polynomial if the error cannot exceed 0.001. f(x) = e^x ≈ 1 + x + x²/2! + x³/3!, x < 0

The explanation of the answer is now provided as follows:

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Taking 4th root of both sided of equation (4), we have:

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Dividing both sides of equation (5) by e^(z/4) gives us:

|x| < 0.3936 / e^(z/4) ……………….................…… (6)

In equation (6), when z > 0, e^(z/4) > 1. Therefore, we have:

|x| < 0.3936 -----> 0 < x < 0.3936

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