Calculus

How is CART impurity cost function minimized?J(k,t_k) = \frac{m_{left}}{m}G_{left}+\frac{m_{right}}{m}G_{right}where G_{left/right} measures the impurity of the left/right subsetand m_{left/right } is...

I've linked an image with the question on.

So author explains how Hard Margin SVM works under the hood(as partially seen on image).But didn't explain what is the idea of minimizing \frac{1}{2}w^TwSo why do we have to minimize it? What is the i...

A line $\vec{L}$ has symmetric equations $\frac{5}{3}x-3 = \frac{4}{3}y + 1 = \frac{1}{3}z + 2$.The point P (0,-1,-2) does not lie on the line. Find the equation of the plane which contains both the l...

Suppose $f(x) \in C^2[0,1]$ such that $f(0)=f(1)=0$, and $f(x)\neq 0$ on $(0,1)$. Prove that\int_0^1 \left| \frac{f''(x)}{f(x)} \right| dx \geq 4.

How do definite integrals give you the area under a curve? I understand how to find the area of a curve for something simple like $y = x^3 - 6x^2 +9x$ between 0 - 3 but my question is why does it work...

How to find derivatives of functions consisting of matrices and vectors? For example:f(x) =x^TA^TAxAs I understand A^TA can be treated as constant? How to treat x^TMy intuition tells me that somehow d...

I understand how to calculate second order directional derivative. I want to get better understanding of the formula of it.So first order directional derivative of f(x,y) in direction of 'u' is:D_uf(x...

Since multivariable vector-valued functions are not covered in Stewart's Calculus I would like to clarify if I understand them correctly. So multivariable vector-valued function looks like this, right...

I will try to mark the exact thing I don't understand, it comes from this thread https://matchmaticians.com/questions/u6me4r#answers :What I don't understand is when we have g(h)=f(x_0+ha,y_0+hb)That...

This time I want to discuss the proof(part of it) of D_uf(x,y)=f_x(x,y)a + f_y(x,y)b, u = <a,b>if we define a function g of the single variable h:g(h)=f(x_0+ha,y_0+hb)then, by definition of deri...

I will give you a part of text taken from the book. Please explain the part where author explains directional derivative: For functions with multiple inputs, we must make use of concept of partial der...

When finding the partial derivative of a multivariable function with respect to one of its variables (let's say x), we treat the other variables (in this case, y) as constant. Does it mean that not de...

Gradient vector is build of partial derivatives of the function of multiple variables. But what is the intuition behind the statement that "gradient vector points in the direction of the steepest incr...

Since I did not get sufficient asnwer I will better ask once again.I'm reading Stewart's Calculus and in "Calculus with Parametric Curves" he shows the formula which comes from the Chain rule:$\frac{d...

I'm reading Stewart's Calculus and in "Calculus with Parametric Curves" he shows the formula which comes from the Chain rule:$\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$But what I don't under...

need this answered before midnight

solve before midnight

need this answered before midnight

The population of beavers can be modeled by a sine function f(x), where x is time in days. at t=0 the number of beavers is at its average of 100, the highest number is measured to be 125. The cycle st...

I'm struggling with connected rates of change $\frac{dy}{dt} =\frac{dy}{dx}\times \frac{dx}{dt}$ I'll give you an example of the type of questions I'm struggling with and I'll explain what I don't und...