Use the first Fundamental Theorem of Calculus and properties of integrals to explain why the following are impossible: 5. J 2t dt 2x2 7. 12t dt 2 CHint: think of x-1) 8. (Section 4.3, 54) Jo f (t) dtx1, no matter what function f is 9, f,f(t) dt x2 + 1, no matter what f and a are

1) In this problem, let x = 2, the value Ax = dx, dy = f'(x)dx, and Ay = f(x + Ax)-f(x) to complete the table f(x)=√x 1.0000 0.5000 0.1000 0.0100 0.0010 2) dx= Ax dy Ay Ay - dy dy Ay 3) 4) f(x) = 5x √2x+3 Find the first derivative given that dy Find X by implicit differentiation. √√x+y+√√x = 4 dx -лr² h A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at the rate of 10 cubic feet per minute, find the rate of change of the depth of the water the instant it is 8 feet deep? 1 V

1. State whether f(x) is differentiable on the entire domain (YES/NO).