Stewart - Calculus 8e ET Chapter 2 Stewart - Calculus 8e ET Chapter 2 Form AForm A © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
- Find Find the the limit.limit.
- Evaluate Evaluate the the limit.limit.
- Find Find the the limit.limit.
- How close How close to 2 to 2 do we do we have to have to taketake x xso so that that is is within within a a distance distance of of 0.01 0.01 from from 13?13?
- If6. If f f and andgg are continuous functions with are continuous functions with
- Find Find the the limit.limit.
- Find Find the the limit.limit.
4.4.How How close close to to do do we we have have to to taketake x xso thatso that
9.9.Find an equation of the tangent line Find an equation of the tangent line to the curve.to the curve. 1 / 4
Stewart - Calculus 8e ET Chapter 2 Stewart - Calculus 8e ET Chapter 2 Form AForm A © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
- 10. Find Find the the limit limit ifif
- 11. Use the Use the graph of graph of the function the function to find to find each limit.each limit.
- 2 3 4 51 2 3 4 5 –1 –1 –2 –2 –3 –3 –4 –4 –5 –5xx
11 22 33 44 55
–1 –1
–2 –2
–3 –3
–4 –4
–5 –5
y y
, , ,,
- 12. Complete Complete the the table table by by computing computing at at the the given given values values ofof x x, accurate to five decimal places., accurate to five decimal places.
- 13. Use the Use the precise definition precise definition of a of a limit limit to prove to prove thatthat
- 14. Find Find the the limit limit ..
- 15. Find Find the the numbers, numbers, if if any, any, where where the the function function is is discontinuous.discontinuous. 2 / 4
Use the results to guess at the indicated limit, if it exists, to three decimal places.Use the results to guess at the indicated limit, if it exists, to three decimal places. x x 3.9 3.9 3.99 3.99 3.999 3.999 4.001 4.001 4.01 4.01 4.14.1
Stewart - Calculus 8e ET Chapter 2 Stewart - Calculus 8e ET Chapter 2 Form AForm A © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
- 16. Find Find the the interval(s) interval(s) where where is is continuous.continuous.
- 17. You You are are given given the the graph graph ofof f f . Find the horizontal an. Find the horizontal and vertical asymptotes of the graph ofd vertical asymptotes of the graph of f f ..
11 2 3 4 5 6 7 2 3 4 5 6 7 –1 –1 –2 –2 –3 –3 –4 –4 –5 –5 –6 –6 –7 –7xx 11 22 33 44 55 66 77
–1 –1
–2 –2
–3 –3
–4 –4
–5 –5
–6 –6
–7 –7
y y 18.18.The graph shows the percentage of households in a The graph shows the percentage of households in a certain city watching television during a 24-hr period oncertain city watching television during a 24-hr period on a wea weekdaekday ( y ( correscorrespondponds to s to 6 a.6 a.m.). m.). By cBy computomputing ing the the slope slope of tof the rhe respecespective tive tangetangent nt line, line, estiestimate mate thethe rate of change of rate of change of the percentage of households watching television at a-12 p.m.the percentage of households watching television at a-12 p.m. Note that Note that 33 dydy
- 2 4 4 6 6 8 8 110 10 12 12 14 14 16 16 18 28 20 0 t t ((hhrr))
0.0750.075
0.150.15
0.2250.225
y (%)y (%)
- 19. Find Find the the derivative derivative of of the the function function and and evaluate evaluate at at the the given given value value ofof x x.. 3 / 4
Stewart - Calculus 8e ET Chapter 2 Stewart - Calculus 8e ET Chapter 2 Form AForm A © 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
- 20. Let Let ..
- / 4
a.a. Sketch the graph of Sketch the graph of f f ..b.b. For what values of For what values of x x is is f f differentiable? differentiable?c.c.Find Find a a formula formula for for ..