### Mathematical Expressions with DiagramsBelow are a series of mathematical expressions involving constants, exponents, and the natural exponential function, paired with box diagrams.#### Expressions1. \(\sqrt{2\pi} \cdot 11^{0 + \frac{1}{2}} \cdots e^{-11} \cdot e^{\frac{1}{{12 \cdot 11}}}\) \\ = ![ ](insert_box_diagram_placeholder) ![ ](ellipsis_placeholder) ...2. \(\sqrt{2\pi} \cdot 12^{1 + \frac{1}{2}} \cdots e^{-12} \cdot e^{\frac{1}{{12 \cdot 12}}}\) \\ = ![ ](second_box_diagram_placeholder) ![ ](ellipsis_placeholder) ...3. \(\sqrt{2\pi} \cdot 13^{2 + \frac{1}{2}} \cdots e^{-13} \cdot e^{\frac{1}{{12 \cdot 13}}}\) \\ = ![ ](third_box_diagram_placeholder) ![ ](ellipsis_placeholder) ...4. \(\sqrt{2\pi} \cdot 14^{3 + \frac{1}{2}} \cdots e^{-14} \cdot e^{\frac{1}{{12 \cdot 14}}}\) \\ = ![ ](fourth_box_diagram_placeholder) ![ ](ellipsis_placeholder) ...5. \(\sqrt{2\pi} \cdot 15^{4 + \frac{1}{2}} \cdots e^{-15} \cdot e^{\frac{1}{{12 \cdot 15}}}\) \\ = ![ ](fifth_box_diagram_placeholder) ![ ](ellipsis_placeholder) ...6. \(\sqrt{2\pi} \cdot 16^{5 + \frac{1}{2}} \cdots e^{-16} \cdot e^{\frac{1}{{12 \cdot 16}}}\) \\ = ![ ](sixth_box_diagram_placeholder) ![ ](ellipsis_placeholder) ...7. \(\sqrt{2\pi} \cdot 17^{6 + \ ## ProblemIn each line, give an approximate value in decimals using a calculator.1. \(\sqrt{2\pi} \cdot 2^{1+\frac{1}{2}} \cdot e^{-2} \cdot e^{\frac{1}{12 \cdot 2}} =\) 1.0003... 2. \(\sqrt{2\pi} \cdot 3^{2+\frac{1}{2}} \cdot e^{-3} \cdot e^{\frac{1}{12 \cdot 3}} =\) 2.0001... 3. \(\sqrt{2\pi} \cdot 4^{3+\frac{1}{2}} \cdot e^{-4} \cdot e^{\frac{1}{12 \cdot 4}} =\) 6.0002...4. \(\sqrt{2\pi} \cdot 5^{4+\frac{1}{2}} \cdot e^{-5} \cdot e^{\frac{1}{12 \cdot 5}} =\) 5. \(\sqrt{2\pi} \cdot 6^{5+\frac{1}{2}} \cdot e^{-6} \cdot e^{\frac{1}{12 \cdot 6}} =\) 6. \(\sqrt{2\pi} \cdot 7^{6+\frac{1}{2}} \cdot e^{-7} \cdot e^{\frac{1}{12 \cdot 7}} =\) 7. \(\sqrt{2\pi} \cdot 8^{7+\frac{1}{2}} \cdot e^{-8} \cdot e^{\frac{1}{12 \cdot 8}} =\) 8. \(\sqrt{2\pi} \cdot 9^{8+\frac{1}{2}} \cdot e^{-9} \cdot e^{\frac{1}{12 \cdot 9}} =\) 9. \(\sqrt{2\pi} \cdot 10^{9+\frac{1}{2}} \cdot e^{-10} \cdot e^{\frac{1}{12 \cdot 10}} =\

Name: ### Mathematical Expressions with DiagramsBelow are a series of mathe
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: ### Mathematical Expressions with DiagramsBelow are a series of mathematical expressions involving constants, exponents, and the natural exponential function, paired with box diagrams.#### Expressions1. \(\sqrt{2\pi} \cdot 11^{0 + \frac{1}{2}} \cdot