intro to calculus

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MATH

220 Written homework #1

Section 1.1

8. f ( x )=4 x 2−3 x +1

14. f ( x )= x/ x^2 −16

15. g ( x )= 8 x −1

44. f ( x )=2 x +4, g ( x )= x ̂ 2−2

Section 1.2

72. Passing through (−3, 7) and (1, 2)

81.2 x +3 y =6

87. f ( x )=3 x − x 3

89. g ( x ) = ( x +3)2 +1

96.Slope = 13, passes through (0, 4)

Section 1.3

119. 7 π/6 rad

124. tan(19 π/4)

129. a =4, c =7

For the following exercises, solve the trigonometric equations on the interval 0 ≤ θ
< 2 π .

155. 2sin θ −1=0

Section 2.1

For the following exercises, points P (1, 2) and Q ( x , y ) are on the graph of the
function f ( x ) = x 2 + 1.

1. [T] Complete the following table with the appropriate values: y -coordinate of Q ,
the point Q ( x , y ), and the slope of the secant line passing through the points P and
Q . Round your answer to eight significant digits.

2. Use the values in the right column of the table in the preceding exercise to guess
the value of the slope of the line tangent to f at x = 1.

3. Use the value in the preceding exercise to find the equation of the tangent line at
point P . Graph f ( x ) and the tangent line.

18. [T] Compute the average velocity of the stone over the given time intervals.

[1, 1.05]

[1, 1.01]
ّ[1, 1.00]
[1, 1.001]

19. Use the preceding exercise to guess the instantaneous velocity of the stone at t
= 1 sec.

Section 2.2

For the following exercises, consider the function

f ( x )= x 2−1. | x − 1|

30. [T] Complete the following table for the function. Round your solutions to four
decimal places.

31. What do your results in the preceding exercise indicate about the two-sided
limit lim f ( x ) x →1

Explain your response?

35. [T] lim sin2 x ; ±0.1, ±0.01, ±0.001, ±.0001 x →0 x

44. lim sin ( π / θ ) θ →0