Documents

CALCULUS PASTHO

Description
Description:
Categories
Published
of 15
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Transcript
  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

a0701e03

Sep 10, 2019
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks
SAVE OUR EARTH

We need your sign to support Project to invent "SMART AND CONTROLLABLE REFLECTIVE BALLOONS" to cover the Sun and Save Our Earth.

More details...

Sign Now!

We are very appreciated for your Prompt Action!

x