A curve is described by y = x . Determine the approximate change in y if x varies from 3 to 3 + 100 .

Step-by-step solution

Given y = x The approximate change in y is given by y dy dx x Here, x = 3 and x = 100 Differentiating y with respect to x , we get dy dx = x At x = 3 , dy dx = ( 3 ) = 1 2 Substituting the values, y 1 2 100 = 200 Using 3.14 , we get y 3.14 200 = 0.0157