 In this video, we provide the solution to question number 10 for the practice final exam for math 1210 We're asked to compute the limit as theta approaches 0 of sine theta over 5 theta squared minus 4 theta My first inclination is because the function is continuous so long as we're inside the domain of the function We're gonna good that is we can just plug in 0 and see what happens 5 times 0 squared minus 4 times 0 on the bottom That's gonna give us 0 in the denominator So we are outside the we are outside the domain of this function But since sine of 0 is likewise 0 we get 0 over 0. This is indeterminate form It turns out this exact question We've already done as a practice question on exam number 3 Because we are able to use limits of trigonometric functions to evaluate this But now that we know Lopi-Tall's rule we could use Lopi-Tall's rule to compute this thing Which might be a more favorable way of computing this one by Lopi-Tall's rule We should take the derivative of the top which will be cosine of theta We should take the derivative of the bottom which will be 10 theta minus 4 Still take the limit as theta approaches 0 which now if we plug in theta equals 0 We're gonna get cosine of 0 which is of 1 actually and then in the denominator We're gonna get 10 times 0 minus 4 so the denominator becomes negative 4 and so we see the correct answer would be choice E