TEST1 - MA 121 TEST 1 Please show all of your work in...

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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 ) = Ì-2 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 Æ-4 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. † † 3 1 3 ...
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