The exponential function e* can be approximated using a Taylor/Maclaurin series 00 e* %3D п! n=0 a) Write a function file that takes x as the input and calculates the approximation of e* using the first six terms of the series. i.e. n = 0 to n = 5. Your function should work for either a scalar or vector inputs. As a check, the approximation should return 42.8667 for x = 4.
The exponential function e* can be approximated using a Taylor/Maclaurin series 00 e* %3D п! n=0 a) Write a function file that takes x as the input and calculates the approximation of e* using the first six terms of the series. i.e. n = 0 to n = 5. Your function should work for either a scalar or vector inputs. As a check, the approximation should return 42.8667 for x = 4.
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![The exponential function e* can be approximated using a Taylor/Maclaurin series
00
x"
п!
n=0
a) Write a function file that takes x as the input and calculates the approximation of e* using the first six terms of
the series. i.e. n = 0 to n = 5. Your function should work for either a scalar or vector inputs. As a check, the
approximation should return 42.8667 for x = 4.
b) The hyperbolic function tanh(x) is defined as
- e-x
tanh(x) =
%3D
ex + e-x
Write an m-file that uses the function file you wrote in part (a) to calculate tanh(x) for x = [1,5, 25, 60]
Calculate the error (absolute difference) between your approximated tanh(x) and the MATLAB's built in tanh()
function. Use the following example fprintf() statement to print the values of the approximated tanh, the
MATLAB's tanh and the absolute error for every input x.
fprintf("x: %.2f, Approximated tanh: %.2f, MATLAB's tanh: %.2f, Absolute error: %.2f\n",
[x;tanh_approx;tanh_real;error])
Example output below.
x: 5.00, Approximated tanh: ???, MATLAB's tanh: ???, Absolute error: ???
x: 25.00, Approximated tanh: ???, MATLAB's tanh: ???, Absolute error: ???
...](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc91eb436-6202-4368-9458-806984f92c1b%2F0080004b-ab12-4f1f-b9a4-752e5aaf5dc6%2F6wsj9z_processed.png&w=3840&q=75)
Transcribed Image Text:The exponential function e* can be approximated using a Taylor/Maclaurin series
00
x"
п!
n=0
a) Write a function file that takes x as the input and calculates the approximation of e* using the first six terms of
the series. i.e. n = 0 to n = 5. Your function should work for either a scalar or vector inputs. As a check, the
approximation should return 42.8667 for x = 4.
b) The hyperbolic function tanh(x) is defined as
- e-x
tanh(x) =
%3D
ex + e-x
Write an m-file that uses the function file you wrote in part (a) to calculate tanh(x) for x = [1,5, 25, 60]
Calculate the error (absolute difference) between your approximated tanh(x) and the MATLAB's built in tanh()
function. Use the following example fprintf() statement to print the values of the approximated tanh, the
MATLAB's tanh and the absolute error for every input x.
fprintf("x: %.2f, Approximated tanh: %.2f, MATLAB's tanh: %.2f, Absolute error: %.2f\n",
[x;tanh_approx;tanh_real;error])
Example output below.
x: 5.00, Approximated tanh: ???, MATLAB's tanh: ???, Absolute error: ???
x: 25.00, Approximated tanh: ???, MATLAB's tanh: ???, Absolute error: ???
...
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