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please I need the solution in Python, thanks in advance Consider the function f:RR defined as f(x)={xsinx,x=01,x=0,notingthatlimx0xsinx=1. (a) Plot f(x) for the interval x[0,10]. (b)

please I need the solution in Python, thanks in advanceimage text in transcribed

Consider the function f:RR defined as f(x)={xsinx,x=01,x=0,notingthatlimx0xsinx=1. (a) Plot f(x) for the interval x[0,10]. (b) Using a bisection method coded explicitly yourself, estimate numerically the first three smallest positive roots of f(x), that is the value(s) x such that f(x)=0. (c) Using a Newton-Raphson method coded explicitly yourself, estimate numerically the first three smallest positive roots of f(x), that is the value(s) x such that f(x)=0. (d) Estimate numerically the integral I=010f(x)dx using a uniform grid of n points and a trapezoidal method coded explicitly yourself. Then, knowing that the value of the integral I is tabulated in the SciPy special function scipy.special.sici (see https://bit.ly/3XoItUb) for its documentation), plot the error of your own estimation of the integral I versus n in semi-log and log scales for n=4,,100. (e) Estimate numerically the integral I by computing the (signed) area in between the y=f(x) curve and the x-axis using a Monte Carlo method with n=10,000 random points generated in the rectangular region given by x[0,10] and y[0.5,1]

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