Lim sin5θ/θ
θ=0
To find the limit of sin(5θ)/θ as θ approaches 0, we can use L'Hôpital's rule. \n\nFirst, we take the derivative of the numerator and denominator with respect to θ: \n\nlim sin(5θ)/θ as θ approaches 0 = lim (5cos(5θ))/1 as θ approaches 0.\n\nNext, we can substitute θ = 0 into the above expression: \n\nlim (5cos(5(0)))/1 = lim 5/1 = 5.\n\nTherefore, the limit of sin(5θ)/θ as θ approaches 0 is 5.