Unformatted text preview: MA 121 TEST 1
Please show all of your work in answering the following: 1. Solve for x : 2 x  x 2 =  x
2 2. Use rules of exponents to give the exact value of 8 3 3. † † equation of the line that contains the points ( 3,7 ) and ( 1, 5 ). Find an 4. Sketch the function † Ïx + 3 x <0 Ô f ( x ) = Ì2 x =0 Ôx2  4x + 3 x > 0 Ó 5. Suppose that $5000 is invested at 8% compounded quarterly. How much money is in your account at the end of 3 years? † 6. Compute the following limits: a) lim
x 2  x  20 x+4 x3  x +1 2x3 + 7 x Æ4 b) lim
x Æ0 x 2  x  20 x+4 c) lim
†
x Æ1 † x 2  x + 20 7. Decide whether f ( x ) = is continuous at x = 0 . Verify your answer. x+4 † 8. Use the definition of derivative to find f ¢( x ) when f ( x ) = x 2  3 x †
† †
†
(OVER) 9. Find y ¢ when a) y = 4 x  x + 2 x
†
5 2 3 2 b) y = ( x 2  2 x )( x 4 + 5 x 2 + 3) 5 c) y =
† 2x 2  5 x x3 + 2 † Ê x ˆ5 d) y = Á 2 ˜ Ë x  1¯
f) y = 2 10. Find y ¢¢¢ when y = x † † e) y = x 2 5 x  1 † x3  x ( x + 3) 4 † 4x 11. Find an equation of the line tangent to the curve y = at the point ( 0,0 ). † 1+ x2 †
12. Given a distance function s( t ) = t  t . Find the velocity and the acceleration at t = 1. † 13. Given a cost function C( x ) = 1000 x 3 + 2 and a revenue function † † R( x ) = 2000 x 2 + 3 , find the marginal profit function.
† †
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This note was uploaded on 03/27/2009 for the course MA MA121 taught by Professor Lada during the Spring '08 term at N.C. State.
 Spring '08
 LADA

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