Answer all the questions below and press submit to see how many you got right.
Differentiable function : A function is called differentiable if $\lim \limits_{h\to 0}\frac{f(x+h)-f(x)}{h}$ exists for every $x.$
Function : A function is a mapping in which every element in one set is mapped to exactly one element of a second set. Most often the mapping is described using a rule. For example the function $f(x)=x+1$ maps 2 to 3 and -1 to 0.
Limit : The limit of a function $f$ for $x$ converging to $x_0$ or $\lim\limits_{x\to 0}f(x)$ is a number $y$ such that for every $\epsilon\gt 0$ there is a $\delta\gt 0$ with $|f(x)-y|\lt\epsilon$ for all $|x-x_0|\lt\delta.$ This means that if $x$ only gets close enough to $x_0$ it will get and stay arbitrarily close to $y.$
Point : A point is an element in a space. Shapes are made of sets of points.
A function is called differentiable in point $a=15$ if which of the following is true?
Combination : In combinatorics a combination is a selection of a subset from a set. There are $\binom{n}{k}$ different combinations that choose $k$ objects out of $n$ possible objects. For example if there is a league with 5 soccer teams, there are $\binom{5}{2}=\frac{5!}{3!2!}=10$ different possible match-ups. In chess a combination is a series of moves that results in a material or positional gain.
Composite function : The composite function $h=f\circ g$ is defined by $h(x)=f(g(x)).$ For example for the functions $f(x)=x^2$ and $g(x)=x+1$ the composite function $h=f\circ g$ is the function $h(x)=(x+1)^2.$ The composite function of two continuous functions is continuous. The composite function of two differentiable functions is differentiable and the derivative can be calculated using the chain rule.
Product : A product is the result of a multiplication.
Sum : A sum is the result of an addition.
Which of the following statements are true for two differentiable functions $f$ and $g$?