This assignment should be completed out-of-class (not in-class). Please email me well before the deadline if you encounter any problems. Also, action will be taken if your file is exactly the same as any other student. Note: if you don’t know how to do part of a question, try to do the other parts.Do everything within a single Maple documentfile (which has extension.mw) and submit the resulting file to blackboard.

1. (a) Determine the following integral. One may need to use a numerical approxima-tion.

∫π/40exp(x3) sin(x4)dx

(b) Using Maple, compute the 5th order Taylor series around x= 0fortanh(sin(x))and plot the accompanying polynomial.

(c) Using Maple, calculate the following sum

N∑n=1M∑m=1(−2)nxn+m

What is the sum for= 3,N= 20andM= 43?

(d) (15 marks) Using Maple, calculate and simplify if possible the inverse of the transpose of E, where Eis given by E=[a−√3ba]For what values of a does the inverse exist?

2. (30 marks) Consider the following polynomial

f(x) = 3×4−4×3−2×2+x+15

UsingMaple, define the function f(x), plot the polynomial for x∈[−1,2], determine its (real)zeros (numerically), and determine its derivative. Also plot in the same graph for f(x)the points(x, f(x))for which the function obtains local minima and maxima, as large red dots.

3. The Fibonacci numbers can be defined as:

Fn=Fn−1+Fn−2

withF0= 0andF1= 1. Alternatively, an explicit expression is Fn=an−(−a)−n√5

witha=1+√52. Plot the points(xn, yn) = (n, Fn)for the first 100 Fibonacci numbers.If you don’t submit the Maple document file with extension.mwfile grading can not be carr