Study guides, Class notes & Summaries

a) Determine the following limits (if they exist): (i) 3 1 6 2 lim 2      x x x (3) (ii) 3 9 lim 2 3      x x x (3) (iii) x x x x x 2 4 2 lim 2     (3) (iv) xx x    1 1 lim 1 (3) (v) 3 9 2 lim  0  x  x x (3) (vi) t t t t sin tan 2 lim 0   (3) (b) Use the Squeeze Theorem to determine the following limit: . 10 5 cos3 lim 2 2     k k k k (3) (c) ...

a) Determine the following limits (if they exist): (i) 3 1 6 2 lim 2      x x x (3) (ii) 3 9 lim 2 3      x x x (3) (iii) x x x x x 2 4 2 lim 2     (3) (iv) xx x    1 1 lim 1 (3) (v) 3 9 2 lim  0  x  x x (3) (vi) t t t t sin tan 2 lim 0   (3) (b) Use the Squeeze Theorem to determine the following limit: . 10 5 cos3 lim 2 2     k k k k (3) (c) ...

MAT1512 EXAM PACK 2023 LATEST QUESTIONS AND ANSWERS 1 [TURN OVER] 2 x 0 3  x  9 x2  x  QUESTION 1 (a) Determine the following limits (if they exist): (i) (3) (ii) x  2 lim 3  x 1 2 (3) x 3 x  9 (iii) (iv) lim x  2x lim 1  x (3) (3) (v) x  1 lim 1  x 2x (3) (vi) lim sin t  tan 2t (3) t  0 t (b) Use the Squeeze Theorem to determine the following limit: 5k 2  cos3k lim 2 . (3)  x  ...

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Use the method of implicit differentiation to determine the derivatives of the following functions: (a) xsin y 1 (5) (5) (c) y (5) (d) y (5) (e) 2y 3xy (5) 3. Determine the equation of the tangent and normal at the given points: