USF MAC2281 Math Calucalus Worksheet

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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.)

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Tags:
limits

Engineering Calculus

Math Calucalus

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