Definition of the Derivative

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Here we’ll practice finding the derivative using limits.

Let $F(w) = w^2$ . Compute

$\lim _{ h\to 0 } \frac {F(2+h)-F(2)}{h} \begin {prompt}=\answer {4}\end {prompt}$

Let $F(y) = 2y-y^2$ . Compute

$\lim _{ h\to 0 } \frac {F(3+h)-F(3)}{h} \begin {prompt}=\answer {-4}\end {prompt}$

Let $y(x) = (x+4)^2$ . Compute

$\lim _{ h\to 0 } \frac {y(1+h)-y(1)}{h} \begin {prompt}=\answer {10}\end {prompt}$

Let $y(\theta ) = (\theta -3)^2$ . Compute

$\lim _{ h\to 0 } \frac {y(1+h)-y(1)}{h} \begin {prompt}=\answer {-4}\end {prompt}$

Let $f(x) = \sqrt {x+3}$ . Compute

$\lim _{ h\to 0 } \frac {f(-1+h)-f(-1)}{h} \begin {prompt}=\answer {\frac {1}{2 \sqrt {2}}}\end {prompt}$

Let $G(x) = \frac {1}{x-4}$ . Compute

$\lim _{ h\to 0 } \frac {G(-1+h)-G(-1)}{h} \begin {prompt}=\answer {-\frac {1}{25}}\end {prompt}$