in each line, give an approximate value in decimals using calulator. ### Mathematics Sequence ProblemsThis content lists several expressions involving exponential and trigonometric functions. Each expression is related to a series of diagrams involving blocks or boxes.#### Expressions and Corresponding Diagrams:1. **Expression (10)**: \[ \sqrt{2\pi} \, 11^{0 + \frac{1}{2}} e^{-11 \, e^{\frac{1}{11 \cdot 12}}} = \] Diagram: - The diagram consists of 10 empty boxes.2. **Expression (11)**: \[ \sqrt{2\pi} \, 12^{1 + \frac{1}{2}} e^{-12 \, e^{\frac{1}{12 \cdot 13}}} = \] Diagram: - The diagram consists of 11 empty boxes.3. **Expression (12)**: \[ \sqrt{2\pi} \, 13^{2 + \frac{1}{2}} e^{-13 \, e^{\frac{1}{13 \cdot 14}}} = \] Diagram: - The diagram consists of 12 boxes, with the last box containing an asterisk (*).4. **Expression (13)**: \[ \sqrt{2\pi} \, 14^{3 + \frac{1}{2}} e^{-14 \, e^{\frac{1}{14 \cdot 15}}} = \] Diagram: - The diagram consists of 13 boxes, with the last three boxes containing asterisks (**).5. **Expression (14)**: \[ \sqrt{2\pi} \, 15^{4 + \frac{1}{2}} e^{-15 \, e^{\frac{1}{15 \cdot 16}}} = \] Diagram: - The diagram consists of 14 boxes, with the last four boxes containing asterisks (**).6. **Expression (15)**: \[ \sqrt{2\pi} \, 16^{5 + \frac{1}{2}} e^{-16 \, e^{\frac{1}{16 \cdot 17}}} = \] Diagram: - The diagram consists of ### Problem**Instructions**: In each line, give an approximate value in decimals using a calculator.1. $\sqrt{2\pi} \ 2^{1+\frac{1}{2}} \ e^{-2} \ e^{\frac{1}{12 \cdot 2}} = \ \boxed{1} \boxed{0} \boxed{0} \boxed{0} \boxed{3} \ \ldots $2. $\sqrt{2\pi} \ 3^{2+\frac{1}{2}} \ e^{-3} \ e^{\frac{1}{12 \cdot 3}} = \ \boxed{2} \boxed{0} \boxed{0} \boxed{0} \boxed{1} \ \ldots $3. $\sqrt{2\pi} \ 4^{3+\frac{1}{2}} \ e^{-4} \ e^{\frac{1}{12 \cdot 4}} = \ \boxed{6} \boxed{0} \boxed{0} \boxed{0} \boxed{2} \ \ldots $4. $\sqrt{2\pi} \ 5^{4+\frac{1}{2}} \ e^{-5} \ e^{\frac{1}{12 \cdot 5}} = \ \boxed{} \boxed{} \boxed{} \boxed{} \ \ldots $5. $\sqrt{2\pi} \ 6^{5+\frac{1}{2}} \ e^{-6} \ e^{\frac{1}{12 \cdot 6}} = \ \boxed{} \boxed{} \boxed{} \boxed{} \ \ldots $6. $\sqrt{2\pi} \ 7^{6+\frac{1}{2}} \ e^{-7} \ e^{\frac{1}{12 \cdot 7}} = \ \boxed{} \boxed{} \boxed{} \boxed{} \ \ldots $7. $\sqrt{2\pi} \ 8^{7+\frac{1}{2}} \ e^{-8} \ e^{\frac{1}{12 \cdot 8}} = \ \boxed{} \boxed{} \boxed{} \boxed{} \ \ldots $8. \(\sqrt{

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Calculus

in each line, give an approximate value in decimals using calulator.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Concept explainers

Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.

Question

in each line, give an approximate value in decimals using calulator.

### Mathematics Sequence Problems

This content lists several expressions involving exponential and trigonometric functions. Each expression is related to a series of diagrams involving blocks or boxes.

#### Expressions and Corresponding Diagrams:

1. **Expression (10)**:
\[
\sqrt{2\pi} \, 11^{0 + \frac{1}{2}} e^{-11 \, e^{\frac{1}{11 \cdot 12}}} =
\]
Diagram:
- The diagram consists of 10 empty boxes.

2. **Expression (11)**:
\[
\sqrt{2\pi} \, 12^{1 + \frac{1}{2}} e^{-12 \, e^{\frac{1}{12 \cdot 13}}} =
\]
Diagram:
- The diagram consists of 11 empty boxes.

3. **Expression (12)**:
\[
\sqrt{2\pi} \, 13^{2 + \frac{1}{2}} e^{-13 \, e^{\frac{1}{13 \cdot 14}}} =
\]
Diagram:
- The diagram consists of 12 boxes, with the last box containing an asterisk (*).

4. **Expression (13)**:
\[
\sqrt{2\pi} \, 14^{3 + \frac{1}{2}} e^{-14 \, e^{\frac{1}{14 \cdot 15}}} =
\]
Diagram:
- The diagram consists of 13 boxes, with the last three boxes containing asterisks (**).

5. **Expression (14)**:
\[
\sqrt{2\pi} \, 15^{4 + \frac{1}{2}} e^{-15 \, e^{\frac{1}{15 \cdot 16}}} =
\]
Diagram:
- The diagram consists of 14 boxes, with the last four boxes containing asterisks (**).

6. **Expression (15)**:
\[
\sqrt{2\pi} \, 16^{5 + \frac{1}{2}} e^{-16 \, e^{\frac{1}{16 \cdot 17}}} =
\]
Diagram:
- The diagram consists of

### Problem

**Instructions**: In each line, give an approximate value in decimals using a calculator.

1. $\sqrt{2\pi} \ 2^{1+\frac{1}{2}} \ e^{-2} \ e^{\frac{1}{12 \cdot 2}} = \ \boxed{1} \boxed{0} \boxed{0} \boxed{0} \boxed{3} \ \ldots $

2. $\sqrt{2\pi} \ 3^{2+\frac{1}{2}} \ e^{-3} \ e^{\frac{1}{12 \cdot 3}} = \ \boxed{2} \boxed{0} \boxed{0} \boxed{0} \boxed{1} \ \ldots $

3. $\sqrt{2\pi} \ 4^{3+\frac{1}{2}} \ e^{-4} \ e^{\frac{1}{12 \cdot 4}} = \ \boxed{6} \boxed{0} \boxed{0} \boxed{0} \boxed{2} \ \ldots $

4. $\sqrt{2\pi} \ 5^{4+\frac{1}{2}} \ e^{-5} \ e^{\frac{1}{12 \cdot 5}} = \ \boxed{} \boxed{} \boxed{} \boxed{} \ \ldots $

5. $\sqrt{2\pi} \ 6^{5+\frac{1}{2}} \ e^{-6} \ e^{\frac{1}{12 \cdot 6}} = \ \boxed{} \boxed{} \boxed{} \boxed{} \ \ldots $

6. $\sqrt{2\pi} \ 7^{6+\frac{1}{2}} \ e^{-7} \ e^{\frac{1}{12 \cdot 7}} = \ \boxed{} \boxed{} \boxed{} \boxed{} \ \ldots $

7. $\sqrt{2\pi} \ 8^{7+\frac{1}{2}} \ e^{-8} \ e^{\frac{1}{12 \cdot 8}} = \ \boxed{} \boxed{} \boxed{} \boxed{} \ \ldots $

8. \(\sqrt{

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