Let f: R² → R be defined as V(x₁, x₂) R² f(x₁, x2) = x₁₂ - 2x₁x² + x₁ - x₁ . a. Find the gradient of f at any (x₁, x2) € R. b. Using Matlab or Octave plot the gradients and iso-curves of f over [-5,4] × [-3,3]. You should submit a printout of the plot and the code that you used to obtain the plot.

solve using PYTHON/matlab

please please help

Plot y = cos x and z = 1- (x^2)/2 + (x^4)/24 on the same  plot. And you can assume x values and then plot on matlab

Can you represent the following Boolean function f(A, B) with a linear classifier? If yes, show the linear classifier. If not, briefly explain why not. f(A, B) A B 1 1 1 1

For the following pairs of functions, first decide whether f(n) dominates g(n), or g(n) dominates f(n); then decide whether f = O(g), or f = Ω(g), or f = Θ(g), and briefly explains. i. f(n)=n2,g(n)=1000n+30 √1 ii. f(n) = n, g(n) = n3 iii. f(n) = 10 log2 n, g(n) = log10(n3) iv. f(n)=n 100 n ,g(n)=1.2 . 4 nn v. f(n)=2 ,g(n)=2.01 .

Recall that the dot product of two vectors (1d matrices) produces a scalar value. The dot product is slightly confusing as the scalar value produced can have an arbitrary meaning that simply represents the mathematical operations of multiplying and summing. In other words, the dot product can simply represent the linear projection of vector onto the number line. This interpretation will be used repeatedly throughout machine learning as our main goal will be to take some features dotted with some weights/parameters. Once again, this can be though of as projecting our features onto a number line where the projection acts as our prediction! Keep this idea in mind as it might not make complete sense as of yet. It also important to know that the dot product can additionally take on other meanings such as a geometric meaning which represents how similar any two vectors are when projected onto one another. Meaning, how much one vector points in the direction of another. Given the following…

Simplify the following Boolean functions using three variable map: e. F(xy.z) E (0,1,2,4,5,6) f. F(x.y.z)%-E (0,1,2,3,6,7)