sample test4 - Math 1ZZ5 1st Sample Test #4 Name:_ (Last...

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Math 1ZZ5 1st Sample Test #4 Name :___________________________________________ (Last Name) (First Name) Student Number: Tutorial Number: _____________________ ____________________ This test consists of 20 multiple choice questions worth 1 mark each (no part marks), and 1 question worth 1 mark (no part marks) on proper computer card filling. All questions must be answered on the COMPUTER CARD with an HB PENCIL. Marks will not be deducted for wrong answers (i.e., there is no penalty for guessing). You are responsible for ensuring that your copy of the test is complete. Bring any discrepancy to the attention of the invigilator. Calculators are NOT allowed. 1. Let , where , , and are differentiable, AÐ=ß >Ñ œ JÐ?Ð=ß >Ñß @Ð=ß >ÑÑ J ? @ ?Ð"ß !Ñ œ #ß ? Ð"ß !Ñ œ #ß ? Ð"ß !Ñ œ 'ß @Ð"ß !Ñ œ $ß @ Ð"ß !Ñ œ &ß @ Ð"ß !Ñ œ %ß J Ð#ß $Ñ œ "ß => = > ? and J Ð#ß $Ñ œ "! A Ð"ß !Ñ @> . Find . (a) (b) (c) (d) (e) % "&" '# )$ % 2. Which of the following differential equations is satisfied by the function ? B C ln ## (a) (b) (c) ? ! # ! ? ! BC BB BC BB BB CC (d) (e) ! # ! BB CC BB CC 3. Find the linearization of at . 0ÐBß CÑ œ C B Ð#ß "Ñ ln (a) (b) (c) """ ### BÐ #ÑC" BÐ #ÑC" BÐ #ÑC" ln ln ln (d) (e) #B  " #B  Ð #ÑC  " ln 4. Find the equation of the tangent plane to the surface at the point . D œ&B C Ð#ß"ß#Ñ (a) (b) (c) D œ %B  #C  ) D œ %B  #C  ) D œ %B  #C  ) (d) (e) D œ %B  #C  ) D œ %B  #C  ' 5. If and changes from to , find the value of the D œ B  BC  $C ÐBß CÑ Ð$ß "Ñ Ð#Þ*'ß !Þ*&Ñ differential . .D (a) (b (c (d (e) ) ) )  ($ "( ($ "( "( "!! "!! "!! "!! "! 6. Find the directional derivative of at the point in the direction 0ÐBß CÑ œ B ÐBCÑ Ð#ß !Ñ sin indicated by the angle . 1 Î$ (a) (b) (c) (d (e ) )  $$ # # # "" " # $ $
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7. Estimate the volume of the solid that lies below the surface and above the rectangle DœBC VœÖÐB ßCÑl!ŸBŸ' ß!ŸCŸ%× Use a Riemann sum with , and take the sample point to be the lower left corner 7 œ $ß 8 œ # of each square. (a) (b) (c) (d) (e) 32 24 16 48 96 8. Set up a double integral which represents the volume under the function and above D œ #BC the triangular region with vertices and . Ð!ß !Ñß Ð"ß #Ñß Ð!ß $Ñ (a) (b) (c)  !B !# B !! " B$ " $ " B$ #BC.C.B (d) ( B B " B " B$ e) 9. Evaluate  #" BC C/ .C.B (a) (b) (c) (d) (e) "" " #% $ ## # # # Ð/ $Ñ Ð/ #Ñ / " / $ Ð/ "Ñ 10. Which of the below integrals is equal to "! #B ln 0ÐBßCÑ.C.B (a) (b) (c)   /" ! / ! " /C B# # C 0ÐBßCÑ.B.C ln ln (d) (e) !/ " C C ln 11. Express the following complex number in polar form. .
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sample test4 - Math 1ZZ5 1st Sample Test #4 Name:_ (Last...

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