Using a symbol-manipulating program such as Maple, Mathematica, MATLAB, or Macsyma, carr...

Using a symbol-manipulating program such as Maple, Mathematica, MATLAB, or Macsyma, carry out the following tasks. Record your work in some manner, for example, by using a diary or script command.

a. Find the Taylor series, up to and including the term x₁₀, for the function (tan x)², using 0 as the point x₀.

b. Find the indefinite integral of (cos x)⁻⁴.

c. Find the definite integral

d. Find the first prime number greater than 27448.

e. Obtain the numerical value of

f. Find the solution of the differential equation y′+y = (1 + ex )⁻¹.

g. Define the function f (x, y) = 9x⁴−y⁴+2y²−1.You want to know the value of f (40545, 70226). Compute this in the straightforward way by direct substitution of x = 40545 and y = 70226 in the definition of f (x, y), using first 6-decimal accuracy, then 7-, 8-, and so on up to 24-decimal digits of accuracy. Next, prove by means of elementary algebra that

Use this formula to compute the same value of f (x, y), again using different precisions, from 6- decimal to 24-decimal. Describe what you have learned. To force the program to do floating-point operations instead of integer arithmetic, write your numbers in the form 9.0, 40545.0, and so forth.