Determine the one-sided limits numerically or graphically. If infinite, state whether the one-sided limits are ∞ or -∞, and describe the corresponding vertical asymptote. limx→2±cos⁡(π2(x−[x]))

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Determine the one-sided limits numerically or graphically. If infinite, state whether the one-sided limits are ∞ or -∞, and describe the corresponding vertical asymptote.  limx→2±cos⁡(π2(x−[x]))

SoosteethicU · Accepted Answer

The floor function gives the result as the largest integer that is less than the number on which this function is applied. It is represented by the expression [x].  The left-side limit of a function at a point is the value of the function obtained at a point very close to the left side of the point. The right-side limit of a function at a point is the value of the function obtained at a point very close to the right side of the point.  The left side limit of the given expression is calculated as follows:  limx→2−cos⁡(π2(x−[x]))=limh→0cos⁡(π2((2−h)−([2−h])))  =limh→0cos⁡(π2(2−h−1))  =limh→0cos⁡(π2(1−h))  =cos⁡(π2)  =0  The right side limit of the given expression is calculated as follows:  limx→2+cos⁡(π2(x−[x]))=limh→0cos⁡(π2((2+h)−([2+h])))  =limh→0cos⁡(π2(2+h−2))  =limh→0cos⁡(π2h)  =cos⁡(0)  =1

Determine the one-sided limits numerically or graphically. If infinite, state wh

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