1. Lab 7 Engineering Applications

2. Application 1: Sum of Series Write a program to calculate the following series: Write your program such that it calculates the series value for 5000 terms. Verify that the series converges to the value  /4 (around 0.7854)

3. Application 2: Finding the minimumx Tension Minimum T Optimal X

4. Finding the Minimum f(x)x 121 72 53 84 135 176

5. Write a program to find the optimal distance x that offers the minimum amount of tension. Start from x = 0.40 m. Use 0.05 m increments. Finding the Minimum

6. Application 3: Area Calculationf(x)

7. Trapezoid Areah a b Area = h * (a + b)/2

8. Area Calculationf(x)

9. Trapezoidal Approximation A1A2A3 x1x2 f(x1) f(x2) Area = A1 + A2 + A3

10. f (x) = 3x 2 –x + 2 x = 1x = 2 Write a program to calculate the area under the curve f (x) = 3x 2 –x + 2 between x = 1 and x = 2 using the Trapezoidal Approximation method (use a small step value) Area Calculation