Answer all the questions below and press submit to see how many you got right.
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 $y.$
Squared : $x$ squared refers to the number $x^2=x\cdot x.$ For example 3 squared equals 9.
$$\lim \limits_{x\to0} \frac{(17+x)^2-17^2}{x}=$$ $$=\lim \limits_{x\to0} \frac{17^2+2\cdot 17\cdot x +x^2-17^2}{x}=$$ $$=\lim \limits_{x\to0} \frac{2\cdot 17\cdot x +x^2}{x}=$$ $$=\lim \limits_{x\to0} 2\cdot 17 +x=?$$
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.
Point : A point is an element in a space. Shapes are made of sets of points.
A function is called differentiable in point $a=8$ if which of the following is true?
$$\lim \limits_{x\to0} \frac{(6+x)^2-6^2}{x}=$$ $$=\lim \limits_{x\to0} \frac{6^2+2\cdot 6\cdot x +x^2-6^2}{x}=$$ $$=\lim \limits_{x\to0} \frac{2\cdot 6\cdot x +x^2}{x}=$$ $$=\lim \limits_{x\to0} 2\cdot 6 +x=?$$