# CALCULUS PASTHO

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Calculus 1 Final Exam Answer Key 1. (5 pts) A B C D E2. (5 pts) A B C D E3. (5 pts) A B C D E4. (5 pts) A B C D E5. (5 pts) A B C D E6. (5 pts) A B C D E7. (5 pts) A B C D E8. (5 pts) A B C D E9. (15 pts) 12  x  + 3 10. (15 pts) 11. (15 pts) 1/(4 π  )  cm/s12. (15 pts) 300  m × 600  m 9  Calculus 1 Final Exam Solutions 1. C. Find the limit.  lim  x → 3 g (  x )   lim  x → 3  x − 4   3 − 4   − 1  Find  f  ( − 1) .   f  ( − 1) = 3( − 1) 2    f  ( − 1) = 3(1)    f  ( − 1) = 3   lim  x → 3  f  [ g (  x )] = 3 2. B. We need to make sure that the piece-wise function is continuous through each domain and at each “break” point (the transition between functions).   x − 3  is continuous over all of  x . 10   The piece-wise function is continuous at the transition  x  =  − 1  since  x  ≤ − 1  for  x − 3 .  1  x  is discontinuous at  x  = 0  which is in the interval − 1 <  x  < 2  The piece-wise function is discontinuous at  x  = 2  since − 1 <  x  < 2  for 1  x  and  x  > 2  for  x  + 2 .   x  + 2  is continuous for all  x  > 2  Therefore the piece-wise function is discontinuous at  x  = 0  and  x  = 2 .3. A. Yes, there’s a zero in the interval [0,1] . Find the limit at the endpoints by plugging the endpoints into the polynomial.   f  (0) = 0 3 + 2(0) − 1 =  − 1    f  (1) = 1 3 + 2(1) − 1 = 2  Since  f  (0) < 0  and  f  (1) > 0 , the Intermediate Value Theorem states that there must be some  x -value in [0,1]  where  f  (  x ) = 0 . This means that there is a zero in the interval [0,1] .4. C. Use the chain rule to find the derivative:  f  ′ ( g (  x )) g ′ (  x )  “derivative of the outside times the derivative of the inside”   f  (  x ) = 4 −  x 2 11

Sep 10, 2019

#### a0701e03

Sep 10, 2019
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