Q. 16 Express the sentence 鈥渢he four... [FREE SOLUTION]

Chapter 2: Q. 16 (page 184)

Express the sentence 鈥渢he fourth derivative of $f (x) = 3 x^{2} - 1$ is equal to $0$ 鈥� in each of the following notations:
(a) prime (b) Leibniz (c) operator

Short Answer

Expert verified

The fourth derivative of $f (x) = 3 x^{2} - 1$ is equal to $0$ in following notations is:

(a) role="math" localid="1648493154402" $\lim_{鈭� x 鈫� 0} (\lim_{鈭� x 鈫� 0} (\lim_{鈭� x 鈫� 0} (\lim_{鈭� x 鈫� 0} \frac{鈭� y}{鈭� x}))) = 0$

(b) role="math" localid="1648493210673" $\frac{d}{d x} (\frac{d}{d x} (\frac{d}{d x} (\frac{d y}{d x}))) = 0$

(c)role="math" localid="1648493260325" $\frac{d}{d x} (\frac{d}{d x} (\frac{d}{d x} (\frac{d}{d x} (3 x^{2} - 1)))) = 0$

Step by step solution

Step 1. Given information

We have been given the fourth derivative of $f (x) = 3 x^{2} - 1$ is equal to $0$ .

Step 2. Part (a) Write the fourth derivative in a prime notation.

$\lim_{鈭� x 鈫� 0} (\lim_{鈭� x 鈫� 0} (\lim_{鈭� x 鈫� 0} (\lim_{鈭� x 鈫� 0} \frac{鈭� y}{鈭� x}))) = 0$

Step 3. Part (b) Write the fourth derivative in a Leibniz notation.

$\frac{d}{d x} (\frac{d}{d x} (\frac{d}{d x} (\frac{d y}{d x}))) = 0$

Step 4. Part (c) Write the fourth derivative in a operator notation.

$\frac{d}{d x} (\frac{d}{d x} (\frac{d}{d x} (\frac{d}{d x} (3 x^{2} - 1)))) = 0$

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Express the sentence 鈥渢he fourth derivative of $f (x) = 3 x^{2} - 1$ is equal to $0$ 鈥� in each of the following notations:
(a) prime (b) Leibniz (c) operator

Short Answer

Step by step solution

Step 1. Given information

Step 2. Part (a) Write the fourth derivative in a prime notation.

Step 3. Part (b) Write the fourth derivative in a Leibniz notation.

Step 4. Part (c) Write the fourth derivative in a operator notation.

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91影视

Express the sentence 鈥渢he fourth derivative of fx=3x2-1is equal to 0鈥� in each of the following notations:(a) prime (b) Leibniz (c) operator

Short Answer

Step by step solution

Step 1. Given information

Step 2. Part (a) Write the fourth derivative in a prime notation.

Step 3. Part (b) Write the fourth derivative in a Leibniz notation.

Step 4. Part (c) Write the fourth derivative in a operator notation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

Mechanics Maths

Statistics

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

Express the sentence 鈥渢he fourth derivative of $f (x) = 3 x^{2} - 1$ is equal to $0$ 鈥� in each of the following notations:
(a) prime (b) Leibniz (c) operator