Questions: Evaluate: lim as h approaches 0 of sin(h) / 8h

Transcript text: Evaluate: $\lim _{h \rightarrow 0} \frac{\sin (h)}{8 h}$

Solution

Solution Steps

To evaluate the limit $\lim_{h \rightarrow 0} \frac{\sin(h)}{8h}$, we can use the well-known limit property $\lim_{h \rightarrow 0} \frac{\sin(h)}{h} = 1$. By factoring out the constant $ \frac{1}{8} $, we can simplify the expression.

Step 1: Define the Limit Expression

We need to evaluate the limit: \[ \lim_{h \rightarrow 0} \frac{\sin(h)}{8h} \]

Step 2: Use Known Limit Property

We use the well-known limit property: \[ \lim_{h \rightarrow 0} \frac{\sin(h)}{h} = 1 \]

Step 3: Simplify the Expression

We can factor out the constant $\frac{1}{8}$ from the limit: \[ \lim_{h \rightarrow 0} \frac{\sin(h)}{8h} = \frac{1}{8} \lim_{h \rightarrow 0} \frac{\sin(h)}{h} \]

Step 4: Apply the Known Limit

Substituting the known limit property: \[ \frac{1}{8} \lim_{h \rightarrow 0} \frac{\sin(h)}{h} = \frac{1}{8} \cdot 1 = \frac{1}{8} \]