Exam Exam

1.- Which of the following sentences is false?

 a) Some integrable functions are continuous functions b) All the integrable functions are continuous functions c) Some continuous functions are derivable functions d) All the derivable functions are continuous functions

2. a) ln (8/3) b) ln8 - ln3 c) (1/2) ln(8/3) d) ln 3

3. a) π b) 0 c) π/2 d) 1

4. a) 1 - √2 b) 3 c) √3 d) √2 - 1

5. The area among the curve y = x3 , the abscissa axis, and the straight lines x = 0 and x = 2 is...

 a) 4 u2 b) 3 u2 c) 2 u2 d) 1/2 u2

6. The area among the curve y = 3x2 – 2x, the abscissa axis, and the straight lines x = 1 and x = 2 is...

 a) 4 u2 b) 8 u2 c) 2 u2 d) 3/2 u2

7. (PAEG- june 2011) The area among the curves: f(x) = 1/x, g(x) = 1/x2 and the straight line x = 2 is...

 a) 1/2 u2 b) ln2 u2 c) (1/2 - ln2) u2 d) (ln2 - 1/2) u2

8. (PAEG - june 2010) The area between the parabolas f(x) = x2 -3x - 1 and g(x) = -x2 + x + 5 is...

 a) 64/3 u2 b) 24 u2 c) 32/3 u2 d) 13/3 u2

9. The volume of the cone generated by the graph of the function y = x spinning around the abscissa axis between 0 and 3 is..

 a) 3π u3 b) 9π u3 c) π u3 d) 2π u3

10. The volume of the solid generated by the graph of the function y = x2 spinning around the abscissa axis between 0 and 1 is...

 a) π/3 u3 b) π/5 u3 c) 2π u3 d) π u3