Solution: The original formula = E x0, 1=e- 1.

5. Find the general solution of differential equation Dy/DX = E (X-Y).

Solution: (e y) dy = (e x) dx separation variable; The result of integration is e y = e x+c, so the general solution is y = ln (e x+c).

Second, solve the problem.

1 1. Find the limit x→3lim[(x? -3x+ 14)/(x？ +5x+4)

Solution: The original formula = 14/28= 1/2.

14. Find the definite integral-1, 1∫(x? -2x？ )dx

Solution: The original formula = [1/4] x? -(2/3)x？ ]- 1, 1=( 1/4-2/3)-( 1/4+2/3)=-4/3

15. Find the general solution y'' =1(1+x? )

Solution: y'=∫dx/( 1+x? )=arctanx+C？ ;

y=∫(arctanx+C？ )dx=xarctanx-ln√( 1+x？ )+C？ x+C？

12. Derive y = 3sinx-2e x+x? - 1

Solution: y' = 3cosx-2e x+2x