Explanation

A metric space is a set with a distance function (metric) that meets three properties: 

1. Non-negativity: Distances are always non-negative.  

2. Symmetry: Distance from A to B equals distance from B to A.  

3.  Triangle Inequality: For any points A, B, and C, the distance from A to C is less than or equal to the sum of the distances from A to B and B to C.  

Explanation

  f(x) = |x| has a cusp at x = 0, making it non-differentiable there.

A function is differentiable at a point if its derivative exists at that point. 

The absolute value function, (f(x)=|x|), has a sharp corner at (x=0). 

Functions with sharp corners are not differentiable at those points.

Explanation

The adjective in the sentence "This is the fast route" is "fast"

Which describes the noun "route". 

An adjective sentence because it contains an adjective modifying a noun.

Explanation

About vpasolve():

It often requires an initial guess to start the numerical search. MathWorks notes this 

It can be used to solve systems of equations. 

It may return only one solution, depending on the equation and parameters

Explanation

This sentence is ambiguous because it does not specify who "he" refers to—Ali or Salman.

Two clear and assertive versions:

1. Ali explicitly stated that he was tired when he met Salman. (This indicates that Ali was the tired one.)

2. When Ali met Salman, Salman clearly said that he was tired. (This indicates that it was Salman who was tired.)

Explanation

The exponential function is its derivative and integral.

The integral of eˣ concerning x.

- The integral of eˣ is eˣ.  

- Don't forget the constant of integration C.

Apply the integration rule for eˣ.

Apply the integration rule:  

∫ eˣ dx = eˣ + C

The integral of eˣ is eˣ + C.

Explanation

To integrate $x^2$, use the power rule of integration:

$$int x^n dx = frac{x^{n+1}}{n+1} + C$$

Here, $n = 2$, so:

$$int x^2 dx = frac{x^{2+1}}{2+1} + C = frac{x^3}{3} + C$$2+1/2+1​+C

=x^3​/3+C