Calculus assignment help
Assignment 1
Complete this assignment after you have finished Unit 1, and submit it for grading. Use the assignment drop box to submit your assignment as a single PDF. Do not submit your assignment by email. If you are unable to use the online drop box, make alternative arrangements with your tutor.
This exercise is worth 5 per cent of your final grade.
1. List the following numbers in increasing order:4 pts
√ 13−
√ 5; 4 √ 38− (
√ 3)−1);
√ 2− 61
152 ; 3π −
√ 5
32 ; π.
2. Fill in the table below. Note that you should refer to the section titled “Intervals,”12 pts on pages 337-338 of the textbook, and to Table 1 on page 338.
Interval Inequality Representation on the real line
x < −3
[−3,∞)
1
4 ≤ x < 12
−13
/
(−25, 7]
3. Identify a real number that belongs to the intersection of each of the sets of2 pts intervals given below.
a. [−2.6,−1) and (−4,−7/4]
b. (π 4 , π
2
] , [ −π 3 , π
3
) and
[π 5 , π
3
]
Mathematics 265: Introduction to Calculus I Assignment 1 1
4. In each of the following exercises, rewrite and simplify the given expression.9 pts Give your answer using positive exponents only.
a. (4x2y4)3/2
b. ( x3
y2
)−4 c. (√
x−5 + x−5y7z−2 ) (x9y−2z9)
5. In each of the following exercises, expand and simplify.12 pts
a. 5(3x− 1) + 4(x2 − 3x+ 3)(x+ 6)
b. (t+ 5)2 − (6t+ 8)(7− t)
c. (1 + 2z − 5x)(z + 5x− 7)
d. (1− a+ 2×2)2
6. In each of the following exercises, perform the indicated operations. Give your6 pts answer as a fraction in lowest terms.
a. 2
x+ 1 − 4 x− 1
b. 3
u+ 3 + u− 2
c. 5
x+ 3 +
1
x2 − 9
d. 2√
x2 + 2 − 5 x2 + 2
7. In each of the following exercises, factor the given expression.8 pts
a. 4×2 − 16t2
b. −10y2 + 31y − 15
c. x3 − 4×2 + 5x− 2
d. 27a3 − 64b3
2 Assignment 1 Mathematics 265: Introduction to Calculus I
8. In each of the following exercises, factor and simplify the given expression.15 pts
a. 9a2 + 24ab+ 16b2
9a2 − 16b2
b. x3 − 8
x2 + 2x− 8
c. x2 + 2×2 − 3x 2×3 + 2×2 − 4x
d. x2y − x2
x3 − x3y
e. x2 + 5x+ 4
x2 − 4x− 5
9. Solve each of the quadratic equations below.12 pts
a. a2 − 6a+ 2 = 0
b. 2×2 + 3x = 2
c. 3×2 = x+ 4
d. 25 = 9×2 − 30x
10. a. Rationalize the denominator of √ 5x− 6√ 5x+ 3
.9 pts
b. Rationalize the numerator of √ 2 + y +
√ 2− y
y .
c. Rationalize the denominator of 2 √ 3 + 1√
6− √ 3
.
11. Convert from radians to degrees the numbers given below. Note that you should3 pts refer to the section titled “Angles” on pages 358-359 of the textbook.
a. 5π
6
b. 3π
8
c. −6π 45
Mathematics 265: Introduction to Calculus I Assignment 1 3
12. Convert from degrees to radians the numbers given below.3 pts
a. −270◦
b. 345◦
c. 38◦
13. Give the exact value of6 pts
a. cos ( 11π
4
) .
b. sin ( 7π
6
) .
c. tan ( 5π
3
) .
Bonus Question In Unit 1 of the Study Guide, we defined the trigonometric functions8 pts using a right triangle with hypotenuse 1. Use similar triangles to define, in any right triangle with hypotenuse z, the trigonometric functions as
cos θ = x
z sin θ =
y
z tan θ =
y
x .
Hint: The circle below has radius 1.
4 Assignment 1 Mathematics 265: Introduction to Calculus I
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