Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. f(x) = x + 4x4 3 , a = −1 lim x→−1 f(x) = lim x→−1 3 = lim x→−1 x + lim x→−1 x4 3 = −1 + 4 4 3 = f(−1) = Thus, by the definition of continuity, f is continuous at a = −1.

Talia took the bus from her home to the bank and then walked back to her home along the same route. the bus traveled at an average speed of 40 km/h and she walked at an average speed of 5 km/h. to determine the time, x, that it took talia to walk home, she used the equation 40(0.9 – x) = 5x. the time of trip 2 is hours. the distance of trip 1 is km.