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EDS107

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###### Mathematics

(1) Calculate the rst derivative f′(x)for each of the following functions. (10 marks, 2 each) (a) f(x)=(5x−4)3, (b) f(x)=√3x−2, (c) f(x)=(7−5x)4/3, (d) f(x)= sin(x) xcos ...

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Maths

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###### Operating System

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###### MATH347-Number Theory

Questions: 1. Answer each of the following statements as true or false. a. If a 3 - 0(mod m), then a - 0(mod m). b. 765432176543217654321765432176543217654321 is divisible by 11. c. x 2 - l(mod 10 ...

Course

MATH347

Type

Home Work

Subject

Maths

University

Winona State University

### Question

Hand your completed assignment in to the correct box in the Student Resource Centre (G40 Building
301) before the due date. Please use a Mathematics Department cover sheet available from the Student
Resource Centre. Don't forget to write down your name (given name as on your ID card), UPI, ID
number. Show all working; answers that do not show their work will typically receive reduced or
zero marks. Late assignments cannot be marked under any circumstances.
This assignment was written by Igor' Kontorovich ([email protected]) and Jesse Hart
([email protected]). The tutors in the Mathematics Assistance Room (in Building 302 Room
170) can give you help and advice, but all work submitted must be your own.
Best of luck!
1. (a) The intervals/statements in (i)-(iii) feature mistakes that are commonly seen. Explain what is
wrong with each of them.
(i) (1;4): (ii) [7;1]: (iii) [8; 9] contains only two numbers.
(b) Simplify the following.
(i) (1; 5) \ f1; 2g: (ii)
(1; 5)n[2; 4]

[ f1; 2g :
[5 Marks]
2. The aim of this problem is to familiarise you with proving and disproving, which are fundamental
ideas in mathematics. For this problem you are given a list of statements and you must determine for
each of them whether the statement is true or false. In mathematics, a statement is true if it holds
for all possible cases that it addresses.
To prove a statement you need to show that it is true in the most general case. You may need to
use variables for this. A statement is false if it does not hold for at least one case. To disprove the
statement you need to provide a single concrete example for which the statement does not hold. You
can nd two worked examples on Canvas!Modules!Course Information.
(a) If a function has a horizontal asymptote, then the function and the asymptote have no intersection.
(b) If a function has a vertical asymptote, then the function and the asymptote have no intersection.
(c) u, v and w are nonzero vectors in R2. If u  v = 0 and v w = 0 then u and w are parallel.
(d) u, v and w are nonzero vectors in R3. If u  v = 0 and v w = 0 then u and w are parallel.
[8 Marks]
3. Sketch the graph for each of the following by hand. Use a separate Cartesian plane (i.e. (x; y)-plane)
for each graph. The x-axis should be the interval [; ] and the y-axis should be chosen appropriately
so that the features of the graph are clear.
(a) f1(x) = (
p
x)2: (b) f2(x) =
p
x2:
(c) f3(x) = xjxj: (d) f4(x) = tan(x) sin(x) cot(x):
Note: similar problems may appear in the test/exam, it is important that you are able to produce such graphs

### Mathematics Department

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## More Mathematics Department: Questions & Answers

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### EDS107 Literacy and Numeracy Across the Curriculum

Questions: 1. Explain the dimensions of the 21st Century Numeracy Model (Goos, Geiger & Dole, 2014). Considerations: What do these dimensions mean? Why is it important for teachers in all subjects to understand this model? of your Numeracy or Goos et al. textbook for a diagram of the model. Cha ...

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### Mathematics

(1) Calculate the rst derivative f′(x)for each of the following functions. (10 marks, 2 each) (a) f(x)=(5x−4)3, (b) f(x)=√3x−2, (c) f(x)=(7−5x)4/3, (d) f(x)= sin(x) xcos(x),(e) f(x)=sin(x2e−2x) ...

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### MATH347-Number Theory

Questions: 1. Answer each of the following statements as true or false. a. If a 3 - 0(mod m), then a - 0(mod m). b. 765432176543217654321765432176543217654321 is divisible by 11. c. x 2 - l(mod 1024) if and only if x _ ±l(mod 1024). d. There are infinitely many odd pseudoprimes to the ba ...

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