Chapter 12, Problem 13PS

To determine

Determine the probable cause of the error.

Answer to Problem 13PS

The values of $x$ has been expressed by the student is in degrees instead of radians.

Explanation of Solution

Given information:

When using a graphing utility to generate a table to approximate $\underset{x\to 0}{\lim }\frac{\tan 2x}{x}$a student concluded that the limit was $0.03491$ rather than $2$ . Determine the probable cause of the error.

Calculation:

Consider the following result obtained by a student:

  $\underset{x\to 0}{\lim }\frac{\tan 2x}{x}$ = $0.03491$

To locate the probable error proceed as follows.

Press $Y=$ and key in the function. The display will be

  

Now press 2^nd window and choose ask. The display will be

  

Noe press 2^nd graph and key in the values of $x$ . The display will be

  

The above result is evaluated by taking the values of $x$ in radians.

The possible error could be due to the fact that the student has expressed the variable in terms of degrees.

To verify the statement, proceed as follows.

Press mode and choose degrees. The display will be

  

Now press 2^nd graph. The display will be

  

Hence, from the above table obtained, it is evident that the values of $x$ has been expressed by the student is in degrees instead of radians