Chapter 6, Problem 10P

Determine the lowest positive root of $f\left(x\right)=7\text{ sin }\left(x\right)e^{-x}-1$:

(a) Graphically.

(b) Using the Newton-Raphson method (three iterations, $x_i=0.3$).

(c) Using the secant method (five iterations, $x_{i-1}=0.5\text{ and }{x}_i=0.4$).

(d) Using the modified secant method (three iterations, $x_i=0.3,\delta =0.01$).