 In this video, we provide the solution to question number nine for practice exam number four for math 1210 We're asked to compete the limit as x approaches pi from the left of x minus pi times cosecant of x now if we just plug in at the pi for x we're gonna get pi minus pi Times cosecant of pi for which you're gonna end up with a zero for pi minus pi But then cosecant at pi remember cosecant is cosine over sine and sine of pi is equal to zero So this thing is gonna look like zero times infinity because pi is a vertical asymptote for cosecant So because we have this indeterminate form we need to use little p-talls rule But as it's zero times infinity we're not quite there yet So we need to change from a product into a quotient the easiest way to do that It's just to push cosecant into the denominator And so this would then become the limit as x approaches pi from the left We're gonna get x minus pi in the numerator and then the reciprocal of cosecant is sine of x So applying low p-talls rule We're gonna take the derivative of top and bottom still taking the limit as x approaches pi from the left the derivative x minus pi It's gonna be one the derivative of sine of x is gonna be cosine of x now if we plug in pi into that situation We get one over cosine of pi cosine of pi It's gonna be negative once you get one over negative one or in other words negative one So we see the correct answer is gonna be