By dragging statements from the left column to the right column below, display a complete calculation of $f'(1)$, where $f(x) = x^2$. As you order the statements, focus on why each statement is true.
Statements to choose from: Drag these statements to the right column.
1. $\displaystyle = \lim_{h\to 0} \frac{(1+h)^2 - 1^2}{h}$
2. $\displaystyle = \lim_{h\to 0} \frac{h(2+h)}{h}$
3. $\displaystyle f'(1) = \lim_{h\to 0} \frac{f(1+h) - f(1)}{h}$
4. $= 2+0 = 2.$
5. $\displaystyle = \lim_{h\to 0} (2+h)$
6. $\displaystyle = \lim_{h\to 0} \frac{2h+h^2}{h}$
7. $\displaystyle = \lim_{h\to 0} \frac{1+2h+h^2 - 1}{h}$
Your solution: Put the statements in order in this column and press the Submit Answers button.
Statements to choose from: Drag these statements to the right column.
1. $\displaystyle = \lim_{h\to 0} \frac{(1+h)^2 - 1^2}{h}$
2. $\displaystyle = \lim_{h\to 0} \frac{h(2+h)}{h}$
3. $\displaystyle f'(1) = \lim_{h\to 0} \frac{f(1+h) - f(1)}{h}$
4. $= 2+0 = 2.$
5. $\displaystyle = \lim_{h\to 0} (2+h)$
6. $\displaystyle = \lim_{h\to 0} \frac{2h+h^2}{h}$
7. $\displaystyle = \lim_{h\to 0} \frac{1+2h+h^2 - 1}{h}$
Your solution: Put the statements in order in this column and press the Submit Answers button.