M-172Q Quiz: MATH 172 Montana State Quiz2

Math 1830 4 Quiz: Quiz 10 Area between curves and consur 3 of 4 (0 complet This Question: 5 pts Find the area between y-3x and y = 2x3 from x-0 to x= The area is (Simplify your answer.)

1 point) Find the limit. Use l'Hospital's Rule if appropriate. Use INF to represent positive infinity, NINF for negative infinity, and D for the limit does not exist. 8x + 8 sinx lim x-0 9x + 9 cosx

Verify that the function is a solution of the differential equation on some interval, for any choice of the arbitrary constants appearing in the function. (a) y=ce2x, y, = 2y 2. (c) y = 5 + ce-x-, y, + 2xy = x 2 y = (I + ce-z?/2); (I-ce-x2/2)-1 2y' + x (y2-1) = 0 y ="e + c2x)ex + sinx + x2, y"-2y' + y -2 cos x + x2-4x + 2 y x-1/2(c1 sinx + c2 cosx) + 4x +8; (d) (f) 2 (h) ty+ (+3-2