Approximate V(2.03)² + (0.8)² + (2.1)² using a linear approximation.

find the intergal of the trig substitutions

Evaluate ¹₁ (y + 1) (y² + 2y)³ dy. Give your answer correct to 2 decimal places.

The deck of a bridge is suspended 285 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by  y = 285 − 16t2. (a) Find the average velocity (in ft/s) of the pebble for the time period beginning when t = 2 and lasting the following amount of time. (i) 0.1 seconds  (ii)0.05 seconds  (iii)0.01 seconds  (b) Estimate the instantaneous velocity (in ft/s) of the pebble after 2 seconds.