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27 results.

Ugur's copy of True/false statements about convergent and divergent series,
Ready to use
Question in Ugur's workspace by Ugur Efem and 1 other

Multiple response question (4 correct out of 8) covering properties of convergent and divergent series and including questions on power series. Selection of questions from a pool.
True/false statements about limits of sequences
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Multiple response question (3 correct out of 6) re properties of convergent and divergent sequences. Selection of questions from a pool.
True/false statements about limits of sequences
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Multiple response question (4 correct out of 8) covering properties of convergent and divergent sequences and boundedness of sets. Selection of questions from a pool.
Find bounds for distance and time spent running, given imprecise measurements
Has some problems
Question in Transition to university by Stanislav Duris and 1 other

Multiplication and division of upper and lower bounds.
When does a sequence get within $d$ of its limit?
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

$x_n=\frac{an^2+b}{cn^2+d}$ . Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| < 10 ^{-r},\;n\geq N$ , $2\leq r \leq 6$ . Determine whether the sequence is increasing, decreasing or neither.
True/false statements about convergent and divergent series,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Multiple response question (4 correct out of 8) covering properties of convergent and divergent series and including questions on power series. Selection of questions from a pool.
Find least upper bounds and greatest lower bounds of four sets
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Four questions on finding least upper bounds and greatest lower bounds of various sets.
Find point when a sequence becomes strictly decreasing
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$x_n=n^k t^n$ where $k$ is a positive integer and $t$ a real number with $0 < t<1$ . Find the smallest integer $N$ such that $(m+1)^k t^{m+1} \leq m^k t^m$ for all $m \geq N$ .
True/false statements about Riemann integration,
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Multiple response question (2 correct out of 4) covering properties of Riemann integration. Selection of questions from a pool.
Least upper bound and greatest lower bound of sets
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Eight questions on finding least upper bounds and greatest lower bounds of various sets.
Determine limit of fractional power sequence
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Question on $\displaystyle{\lim_{n\to \infty} a^{1/n}=1}$ . Find least integer $N$ s.t. $\ \left |1-\left(\frac{1}{c}\right)^{b/n}\right| \le10^{-r},\;n \geq N$
Find limit of a sequence
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Let $x_n=\frac{an+b}{cn+d},\;\;n=1,\;2\ldots$ . Find $\lim_{x \to\infty} x_n=L$ and find least $N$ such that $|x_n-L| \le 10^{-r},\;n \geq N,\;r \in \{2,\;3,\;4\}$ .
Find limits of sequences
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Seven standard elementary limits of sequences.
Finding limits by substitution,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Using simple substitution to find $\lim_{x \to a} bx+c$ , $\lim_{x \to a} bx^2+cx+d$ and $\displaystyle \lim_{x \to a} \frac{bx+c}{dx+f}$ where $d\times a+f \neq 0$ .
True/false statements about limits of sequences
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Multiple response question (4 correct out of 8) covering properties of convergent and divergent sequences and boundedness of sets. Selection of questions from a pool.
When is a sequence within d of its limit?
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$x_n=\frac{an+b}{cn+d}$ . Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| \le 10 ^{-r},\;n\geq N$ , $2\leq r \leq 6$ .
Bivariate continuous distribution - marginals and conditional probability,
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$f(x,y)$ is the PDF of a bivariate distribution $(X,Y)$ on a given rectangular region in $\mathbb{R}^2$ . Write down the limits of the integrations needed to find $P(X \ge a)$ , the marginal distributions $f_X(x),\;f_Y(y)$ and the conditional probability $P(Y \le b|X \ge c)$
True/false statements about continuity and differentiability,
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Multiple response question (2 correct out of 4) covering properties of continuity and differentiability. Selection of questions from a pool.

Can choose true and false for each option. Also in one test run the second choice was incorrectly entered, rest correct, but the feedback indicates that the third was wrong.
True/false statements about properties of continuity and limits,
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Multiple response question (2 correct out of 4) covering properties of continuity and limits of functions. Selection of questions from a pool.
Find least upper bounds and greatest lower bounds of various sets
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Eight questions on finding least upper bounds and greatest lower bounds of various sets.
Limits of accuracy in measuring weight in a gym scenario
Ready to use
Question in Transition to university by Stanislav Duris and 1 other

Work with lower and upper bounds for estimates of weight.
Sequences and Limits 1.3
Ready to use
Question in Bill's workspace by Bill Foster

$x_n=\frac{an+b}{cn+d}$ . Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| \lt 10 ^{-r},\;n\geq N$ , $2\leq r \leq 6$ .
Sequences and Limits 1.2
Ready to use
Question in Bill's workspace by Bill Foster

Let $x_n=\frac{an+b}{cn+d},\;\;n=1,\;2\ldots$ . Find $\lim_{x \to\infty} x_n=L$ and find least $N$ such that $|x_n-L| \lt 10^{-r},\;n \geq N,\;r \in \{2,\;3,\;4\}$ .
Sequences and Limits 1.1
Ready to use
Question in Bill's workspace by Bill Foster

Seven standard elementary limits of sequences.
Max and Min 5
Ready to use
Question in Bill's workspace by Bill Foster

$I$ compact interval. $\displaystyle g: I \rightarrow I, g(x)=\frac{ax}{x^2+b^2}$ . Find stationary points and local maxima, minima. Using limits, has $g$ a global max, min?
Max and Min 4
Ready to use
Question in Bill's workspace by Bill Foster

$g: \mathbb{R} \rightarrow \mathbb{R}, g(x)=\frac{ax}{x^2+b^2}$ . Find stationary points and local maxima, minima. Using limits, has $g$ a global max, min?
Katie's copy of Sequences and Limits 1.1
Ready to use
Question in Katie's workspace by Katie Dexter

Seven standard elementary limits of sequences.

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