matlab Answer all parts

4) Create MatLab Function program(s): Approximating the hyperbolic sine function The hyperbolie sine finction is defined stnh(e)-e- Using Taylor's formula and a bit of algebra, it can be shown that where and an . 2n(2n+1) an-1 Note that this last relationship expressing a. in terms of a,ri is called a recurrence relationship. As in the previous example, the accuracy of this approximation depends on how large Nis. Additionally, this approximation is better for x values that are close to zero, regardless of the magnitude of N. Numerical experiment: 1. 2. 3. Compare results (discus, anslysis the error) in the approximate results to the effectively 'true Write a function that approximates sinh(x) using the formula above. Make this function work with a vector x input. Generate plots of the approximate sinh function for N-0,1,2,3. In each plot x should range between 0 and 3. result which is assumed as the built-in MatLab version of sinh) Additional Questions (for memo discussio): 1. In this example, how many parameters control the accuracy or truncation error of the approximation? 2. Extra: Suggest (and if possible program) a good method for estimating sinh(x), e.g using an appropriate number of terms and suitable convergence approach