57 results for "domain".
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Question in MY QUESTIONS
Given a randomised log function select the possible ways of writing the domain of the function.
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Question in MY QUESTIONS
Given a randomised square root function select the possible ways of writing the domain of the function.
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Question in MY QUESTIONS
Given a randomised rational function select the possible ways of writing the domain of the function.
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Question in MY QUESTIONS
Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.
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Question in Content created by Newcastle University
Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$ with coefficients in the real numbers. Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by: \[\phi(p(x))=p(a)+p(bx+c).\]Using the standard basis for range and domain find the matrix given by $\phi$.
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Question in Content created by Newcastle University
Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$ with coefficients in the real numbers.
Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by:
$\phi(p(x))=ap(x) + (bx + c)p'(x) + (x ^ 2 + dx + f)p''(x)$
Using the standard basis for range and domain find the matrix given by $\phi$.
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Question in College Algebra for STEM
Given a randomised rational function select the possible ways of writing the domain of the function.
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Question in College Algebra for STEM
Given a randomised log function select the possible ways of writing the domain of the function.
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Question in College Algebra for STEM
Given a randomised square root function select the possible ways of writing the domain of the function.
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Question in Trignometry
Multiple choice questions. Given randomised trig functions select the possible ways of writing the domain of the function.
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Question in Trignometry
Multiple choice questions. Given randomised trig functions select the possible ways of writing the domain of the function.
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Question in Maths support
Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$ with coefficients in the real numbers.
Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by:
$\phi(p(x))=ap(x) + (bx + c)p'(x) + (x ^ 2 + dx + f)p''(x)$
Using the standard basis for range and domain find the matrix given by $\phi$.
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Question in Maths support
Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$ with coefficients in the real numbers. Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by: \[\phi(p(x))=p(a)+p(bx+c).\]Using the standard basis for range and domain find the matrix given by $\phi$.
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Question in MY QUESTIONS
Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.
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Question in MY QUESTIONS
Multiple choice questions. Given randomised trig functions select the possible ways of writing the domain of the function.
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Question in MY QUESTIONS
Multiple choice questions. Given randomised trig functions select the possible ways of writing the domain of the function.
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Question in Linear Algebra
Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$ with coefficients in the real numbers. Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by: \[\phi(p(x))=p(a)+p(bx+c).\]Using the standard basis for range and domain find the matrix given by $\phi$.
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Question in Linear Algebra
Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$ with coefficients in the real numbers.
Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by:
$\phi(p(x))=ap(x) + (bx + c)p'(x) + (x ^ 2 + dx + f)p''(x)$
Using the standard basis for range and domain find the matrix given by $\phi$.
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Question in Joshua's workspace
Multiple choice question. Given a randomised polynomial select the possible ways of writing the domain of the function.
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Question in LSE MA100 (Bugs fixed, September 2018)
This is the question for week 3 of the MA100 course at the LSE. It looks at material from chapters 5 and 6. The following describes how two polynomials were defined in the question. This may be helpful for anyone who needs to edit this question.
In part a we have a polynomial. We wanted it to have two stationary points. To create the polynomial we first created the two stationary points as variables, called StationaryPoint1 and StationaryPoint2 which we will simply write as s1 ans s2 here. s2 was defined to be larger than s1. This means that the derivative of our polynomial must be of the form a(x-s1)(x-s2) for some constant a. The constant "a" is a variable called PolynomialScalarMult, and it is defined to be a multiple of 6 so that when we integrate the derivative a(x-s1)(x-s2) we only have integer coefficients. Its possible values include positive and negative values, so that the first stationary point is not always a max (and the second always a min). Finally, we have a variable called ConstantTerm which is the constant term that we take when we integrate the derivative derivative a(x-s1)(x-s2). Hence, we can now create a randomised polynomial with integers coefficients, for which the stationary points are s1 and s2; namely (the integral of a(x-s1)(x-s2)) plus ConstantTerm.
In part e we created a more complicated polynomial. It is defined as -2x^3 + 3(s1 + s2)x^2 -(6*s1*s2) x + YIntercept on the domain [0,35]. One can easily calculate that the stationary points of this polynomials are s1 and s2. Furthermore, they are chosen so that both are in the domain and so that s1 is smaller than s2. This means that s1 is a min and s2 is a max. Hence, the maximum point of the function will occur either at 0 or s2 (The function is descreasing after s2). Furthermore, one can see that when we evaluate the function at s2 we get (s2)^2 (s2 -3*s1) + YIntercept. In particular, this is larger than YIntercept if s2 > 3 *s1, and smaller otherwise. Possible values of s2 include values which are larger than 3*s1 and values which are smaller than 3*s1. Hence, the max of the function maybe be at 0 or at s2, dependent on s2. This gives the question a good amount of randomisation.
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Question in Nicholas's workspace
I created this question, and every other question in Multiple Integration, for my dissertation `Computer-Aided Assessment of Multiple Integration'.
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Question in MTH1000 worksheets
No description given
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Question in Pascal's workspace
No description given
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Question in Functions
Multiple choice questions. Given randomised trig functions select the possible ways of writing the domain of the function.
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Question in Functions
Multiple choice questions. Given randomised trig functions select the possible ways of writing the domain of the function.
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Question in Sanka's workspace
Finding domain and range of a given function.
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Question in Sanka's workspace
Find the domain of a function.