Mathematical functions can sometimes be used to generate interesting shapes or patterns. 

 

Mathematical functions can sometimes be used to generate interesting shapes or patterns. The function f(x) sin x /x is generally known as the cardinal sine function (sinc) which has an oscillatory and decaying pattern as illustrated in Figure 1. This function is everywhere continuous except one point, where x = a. Identify this point (value of a) where the function is discontinuous. From what you have learned, despite the discontinuity at x a, it is possible that the limit of this function exists at a. Using the L'Hopital's rule, determine this limit, lim xa f(x). fx.y)- sin (x^2)+y^2)+(c^2)(1 /2) ) / (x^2)+(y^2)+(c^2)^(1/2)) With your knowledge in differentiation techniques, determine the expressions of partial derivatives fx and fy c 6 At this point it is probably clear that f(x) is basically a simplified vertical slice of the surface f(x, y). Taking the slice of f(x,y) where y 0, determine the first non-zero position of x (value of x other than x ripple has horizontal gradient (fx 0) 0) where this =