Description

1 attachmentsSlide 1 of 1attachment_1attachment_1

Unformatted Attachment Preview

MAC 2281 – Engineering Calculus I – Worksheet 1

Name_________________________

Complete the worksheet on a separate sheet of paper. Solve each of the questions below. The

worksheet worth 100 points. Show all work.

In questions 1-8 and 11-13, use algebraic methods to evaluate the limit.

1

2

1. ! lim

y→2

3

3

2y − y +

2

2.! lim

θ →0

10. Given the function ! y =

7 + sec 2 θ

2 ⋅ 4θ

11. ! lim

3x − 1

x→1/3 9x 2 − 1

3.! lim

4 + 6t + 2t 2

4.! lim 2

t→−1 4t − 4t − 8

1

3

+

5. ! lim 2x − 5 15 + 3x

x→0

3x

6. ! lim

x→4

4−x

5 − x2 + 9

sin 2 x

x→∞

x2

7. ! lim

8. ! lim

x→0

2x

, use limits

x −1

to find the behavior of the function around its

asymptotes.

y2 − y −

1− cos x

(Hint: Use the conjugate.)

x2

9. Find the values ! a and ! b so that ! f is

continuous on ! ( −∞,∞ ) :

⎧ ax + 2b

x≤0

⎪ 2

! f ( x ) = ⎨ x + a − 4b 0 < x ≤ 2
⎪ −3x 3 + 5
x>2

⎩

2

x −1 + x −4

x→∞ x −2 − x −3

12. ! lim

x→−∞

4 − 3x 3

x6 + 9

13. ! lim t 2 + t − t 2 − t

t→∞

x2

, use the limit

x3 − 4

definition of the derivative to find ! g′ ( x ) .

14. Given ! g ( x ) =

15. Find the equation of the tangent line to the

curve ! f ( t ) = 3t 2 − 4t 4 at ! t = −1 , using the

limit definition of the derivative.

16. Find the equation of the tangent line to the

curve ! y = 3 x at the point ! ( x, y ) = (1,1) , using

the limit definition of the derivative. (Hint:

Use the difference of perfect cubes.)

Purchase answer to see full

attachment

Tags:

limits

Engineering Calculus

Math Calucalus

User generated content is uploaded by users for the purposes of learning and should be used following Studypool’s honor code & terms of service.

## Reviews, comments, and love from our customers and community:

This page is having a slideshow that uses Javascript. Your browser either doesn't support Javascript or you have it turned off. To see this page as it is meant to appear please use a Javascript enabled browser.