Chapter 11.2, Problem 84PE

(a)

To determine

The error in the equation ${\left(x+h\right)}^3-x^3=x^3+h^3-x^3=h^3$ and correct the error if possible.

(b)

To determine

The error in the equation $\frac{1}{a+b}=\frac{1}{a}+\frac{1}{b}$ and correct the error if possible.

(c)

To determine

The error in the equation $\frac{1}{a+b}=\frac{1}{a}+b$ and correct the error if possible.

(d)

To determine

The error in the equation $\sqrt{x+h}-\sqrt{x}=\sqrt{x}+\sqrt{h}-\sqrt{x}=\sqrt{h}$ and correct the error if possible.

(e)

To determine

The error in the equation $\frac{\sin 2x}{x}=\sin 2$ and correct the error if possible.

(f)

To determine

The error in the equation $\frac{a+bx}{a}=1+bx$ and correct the error if possible.

(g)

To determine

The error in the equation $\underset{x\to 1}{\lim }\frac{x^3-1}{x-1}=\frac{1^3-1}{1-1}=\frac{0}{0}=1$ and correct the error if possible.

(h)

To determine

The error in the equation $\sin \left(x+h\right)-\sin x=\sin x+\sin h-\sin x=\sin h$ and correct the error if possible.

(i)

To determine

The error in the equation $ax=bx,\text{so }a=b$ and correct the error if possible.

(j)

To determine

The error in the statement,'' To find $\underset{x\to 4}{\lim }\frac{x^2-9}{x-3}$, it is necessary to rewrite $\frac{x^2-9}{x-3}$ by factoring $x^2-9$" and if possible correct the error.