A robot is guided towards an object by a software algorithm that controls its position such that the path of the robot is approximately sinusoidal, with a period 2, as shown in Figure B4 (attached).

(a) Show that the length l of any single-variable function f(x), between the limits of x=a and b, can be expressed by the following integral (attached)

This solution involves how to show that the length l of any single-variable function f(x), between the limits of x=a and b, can be expressed by the given integral.

... are independent, the joint probability distribution function is simply the multiplication of the two independent single-variable distribution functions: ...

... For example: x² 10x = 0 is a single variable equation, whereas 2x + 3y = 10 is ... A function is always an equation, but not all equations are functions. ...

... Similar is the situation with functions of two variables f ... have to calculate the limit of a function f(x ... In contrast to the case of a single variable where there ...

... most simple case - both ends are kept at The system becomes: (1.6) We assume we can write the function as a product of two single-variable functions: (1.7) So ...

... If a company is using a single variable input (labor) and a given amount ... output increases by less than 100%, is the company's production function exhibiting a ...

... a constant and (the first power of) a single variable. ... example, vertical lines are not functions because for ... which contradicts with the definition of function. ...

... From the 1990's on, the discount rate has been a function of the target Federal ... But if the Fed's mandate can be drawn directly back to a single variable it has ...

... "How bright someone is, is the single variable that has ... school curriculum are only 50-50, and he or she will have a hard time functioning independently without ...

... 1.20) The boundary conditions are: (1.21) To solve this equation we set the wave function as a product of single variable independent functions: (1.22) When we ...

... The transition function is a mapping Q x [Sigma] -> Q x {L,R,U,D} to ... Since b is a single variable, this implies that in any such assignment b has to be set true ...