answer thsi question:Write a program that answers the following questions. The program must be in $.$ipynb format, and runnable in Google Colab. In the program use separate code blocks to answer each question. The answers must be printed when the program runs.

Problem $-$ Assume the following nonlinear function. $=$ sin $+2$ cos$2$

Prepare a python program to estimate it$.$ Consider the following in your program:

$1)$ Select two hidden layers where the first hidden layer has $6$ neurons, and the second hidden layer has $4$ neurons.

$2)$ Generate $30$ random value for $$ in the range of $=[0,]$ and calculate the correct output of that according to the above equation. Consider these $30$ samples as the training data set and train the neural network with these data. Use Mean Square Error for loss function, Adam for optimization and train the NN for $20$ epochs.

$3)$ Generate $20$ more data points in the range of $[0,]$ for testing the quality of NN$.$ Let$$s call the correct outputs y$.$ Calculate the prediction of your NN for these values $($call them yhat$)$ and compare them with the correct output value y$.$ Plot both y and yhat versus input x at the same figure.

$4)$ Generate $20$ more data in the range of $[,2]$ and add them to the test data set generated in step $3.$ Repeat step $4$ and plot y and yhat for the whole test data set. Does your NN have extrapolation capability? $($Answer that in a text box appeared after the figure in your program$)$