Chapter 9.2, Problem 9QR

To determine

To Write: A function in $x$ as a function of $h\left(=\frac{1}{x}\right)$

Answer to Problem 9QR

The function transformed into the variable $h$ is $y=\frac{\sin h}{h}$

Explanation of Solution

Given Information: The function is $y=x\sin \frac{1}{x}$

Method: Manipulate the expression algebraically to write it in terms of $\frac{1}{x}$ and then replace $\frac{1}{x}$ with $h$ .

Multiply the numerator and the denominator of the expression by $\frac{1}{x}$ to write

  $y=x\sin \frac{1}{x}=\frac{\frac{1}{x}\cdot x\sin \frac{1}{x}}{\frac{1}{x}}$

  $=\frac{1\cdot \sin \frac{1}{x}}{\frac{1}{x}}=\frac{\sin \frac{1}{x}}{\frac{1}{x}}$

Now, in the expression, replace $\frac{1}{x}$ with $h$ to write

  $y=\frac{sinh}{h}$