A continuous function is a function whose value of function at a point is equals to the value of limit at that same point. We can write the condition of continuity as: {eq}\displaystyle { g(b) = \lim_{x \to b} g(x) } {/eq} ...
How to check if a function is convex?Convexity And Concavity Of A function:If a function f(x) is twice differentiable, then the value of the secodn derivative tells us the following, f″(x)>0 then the function is convex f″(x)<0 then the function is concave...
Math: How to Find the Tangent Line of a Function in a Point Another application is finding extreme values of a function, so the (local) minimum or maximum of a function. Since in the minimum the function is at it lowest point, the slope goes from negative to positive. Therefore, the d...
If a function isdifferentiableand in just one variable, the condition number can be calculated from thederivativeand is given by (xf′)/f. So the condition number ofexwill be x, and can be as large as therangeof x. The condition number of ln(x) for every point x is 1/ln(x). ...
Let g(x) and h(y) be differentiable functions, and let f(x, y) = h(y)i+ g(x)j. Can f have a potential F(x, y)? If so, find it. You may assume that F would be smooth. (Hint: Consider the mixed partial derivatives of F.) How to answer this question? W...
... then we can write down the Weierstraß equation simply for this given function. How to compute the derivative given the derivative of f is another question. If f−1 is given, then we do not have to bother about f. How do you know the inverse is differentiable? Apr 21, 2019...
Stationary point of a function is a point where the derivative of a function is equal to zero and can be a minimum, maximum, or a point of inflection
One possibility is to use ANNs to obtain an approximate solution to the value function of the HJB equation24,26. An alternative method is based on the solution of Pontryagin’s maximum principle via differentiable programming27. Control approaches that rely on Pontryagin’s maximum principle ...
How to find an isomorphism between the two groups? How to express a function as the composition of spherical harmonics? Determine whether the following function f: G → H is an isomorphism: f(x) = \sqrt{x}, where G = R^+ under multiplication and H = R^+ under multiplication. ...
that you can find the limit of an infinite number of tiny rectangles below a curve (a.k.a.Riemann sums). Absolute integration has amore rigid requirement:in addition to being able to find an integral, you must also be able to find the integral for the absolute values of the function. ...