Question

Please solve and explain this...

Answer 1

Correct option: c. 8

Explanation:

One-sided Limit

Given a piecewise function, we can find the limit when the variable approaches a specific value in the boundary of two pieces.

Special care must be taken to determine what function will be used to calculate the limit according to the conditions of the independent variable.

The given function p(t) has 3 pieces or subfunctions according to different conditions of t. We need to calculate:

`\lim _(x\to 2^(-))p(t)`

We must find the subfunction where a value of t is close to 2 but is less than 2.

The correct subfunction is

`p(t)=t^3\qquad -2\le t\le 2`

Taking the limit:

`\lim _(x\to 2^(-))p(t)=\lim _(x\to 2)t^3=2^3=8`

Correct option: c. 8