Differentiation

Answer all the questions below and press submit to see how many you got right.

id: 17623

$$\lim \limits_{x\to0} \frac{(17+x)^2-17^2}{x}=$$ $$=\lim \limits_{x\to0} \frac{17^2+2\cdot 17\cdot x +x^2-17^2}{x}=$$ $$=\lim \limits_{x\to0} \frac{2\cdot 17\cdot x +x^2}{x}=$$ $$=\lim \limits_{x\to0} 2\cdot 17 +x=?$$

id: 17583

A function is called differentiable in point $a=8$ if which of the following is true?

  • The limit $\lim \limits_{x\to a}f(x)$ exists.
    The limit $\lim \limits_{x\to 0}\frac{f(8+x)-f(8)}{x}$ exists.
    $\lim \limits_{x\to 8}f(x)=f(8).$
    $\lim \limits_{x\to 0}\frac{f(x+8)-f(x)}{x}=f(8).$
id: 17612

$$\lim \limits_{x\to0} \frac{(6+x)^2-6^2}{x}=$$ $$=\lim \limits_{x\to0} \frac{6^2+2\cdot 6\cdot x +x^2-6^2}{x}=$$ $$=\lim \limits_{x\to0} \frac{2\cdot 6\cdot x +x^2}{x}=$$ $$=\lim \limits_{x\to0} 2\cdot 6 +x=?$$