Randolph College
Department of Mathematics and Computer Science

 

Homework # 8 - Math 149


The problems on this homework must be done alone.  The honor code is in effect.

 First name:   Last name:


 

1.  On what line is the first error in the following? Let \(f(x) = 4x^2\).

$$\begin{array}{rclr} f'(x) & = & \lim_{h \rightarrow 0} \frac{f(x+h) - f(x)}{h}\hspace{.5 in} & \mbox{Line 1}\\ & = & \lim_{h \rightarrow 0} \frac{4x^2 + h - 4x^2}{h} & \mbox{Line 2}\\ & = & \lim_{h \rightarrow 0} \frac{h}{h} & \mbox{Line 3}\\ & = & \lim_{h \rightarrow 0} 1 & \mbox{Line 4}\\ & = & 1 & \mbox{Line 5} \end{array}.$$

a.  Line 1.

b.  Line 2.

c.  Line 3.

d.  Line 4.

e.  Line 5.

 

2.  On what line is the first error in the following? Let \(f(x) = x^3\).

$$\begin{array}{rclr} f'(x) & = & \lim_{h \rightarrow 0} \frac{f(x+h) - f(x)}{h}\hspace{.5 in} & \mbox{Line 1}\\ & = & \lim_{h \rightarrow 0} \frac{(x+h)^3 - x^3}{h} & \mbox{Line 2}\\ & = & \lim_{h \rightarrow 0} \frac{x^3 + h^3 - x^3}{h} & \mbox{Line 3}\\ & = & \lim_{h \rightarrow 0} \frac{h^3}{h} & \mbox{Line 4}\\ & = & \lim_{h \rightarrow 0} h^2 & \mbox{Line 5}\\ & = & 0^2 & \mbox{Line 6}\\ & = & 0 & \mbox{Line 7} \end{array}.$$

a.  Line 1.

b.  Line 2.

c.  Line 3.

d.  Line 4.

e.  Line 5.