Seven standard elementary limits of sequences. 

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 $|x_n-L| \lt 10^{-r},\;n \geq N,\;r \in \{2,\;3,\;4\}$.

$x_n=\frac{an+b}{cn+d}$. Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| \lt 10 ^{-r},\;n\geq N$, $2\leq r \leq 6$.

Given a set in predicate form i.e. $A=\{x|P(x)\}$, find and input the elements of the set.

Given a set $A$, elements of which may also be sets, determine if the given elements or subsets are in $A$.

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

Enumerate elements of a set given in predicate form.

For example, find all elements of $A=\{x\in\mathbb{Z}\;|\;\;|2x-5|<4\}$.

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Implicit differentiation.

Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.

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Students enter equation and turning point

English sentences which are propositions are given and for each the appropriate statement involving quantifiers is to be chosen. 

English sentences which are propositions are given and the appropriate logical expression chosen for the negation of the sentence.

English sentences are given and for each the appropriate statement involving quantifiers is to be chosen. Also choose whether the statements are true or false.

Quotient and remainder, polynomial division.

a) Given a recursively defined sequence $t(n)$, find $t(n)$ as a function of $n$.

b) Given a sequence $s(n),\;n \in \mathbb{N}$, find a recursive definition of $s(n)$

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$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

The random variable $X$ has a PDF which involves a parameter $c$. Find the value of $c$. Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$.

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Quotient and remainder, polynomial division.

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Given sentences involving propositions translate into logical expressions.

Asks to determine whether or not 6 statements are propositions or not i.e. we can determine a truth value or not.

Various questions on predicates and sets.