find f(x) using the formal definition of a limit and proper limit notation

Find f’(x) using the formal definition of a limit and proper limit notation.

State, with reasons, the valuesof x where f(x), shown below,is not differentiable.

Find the slope of the line that is normal to f(x) at the point(-1, 2).

Find f’(x).

Find dy/dx.

A particle’s motion is describedby the following function:

where s is measured in feet and t is measured in seconds.

Find the average velocity of theparticle over the first 5 seconds.

A particle’s motion is describedby the following function:

where s is measured in feet and t is measured in seconds.

Find the speed of the particle at 7 seconds.

A particle’s motion is describedby the following function:

where s is measured in feet and t is measured in seconds.

When does the particle changedirection?

A particle’s motion is describedby the following function:

where s is measured in feet and t is measured in seconds.

Find the the total distance theparticle covers in the first 5 seconds.

Find all points of discontinuity.

Solve the following equationalgebraically. Give approximateanswers rounded to the nearestthousandth.

Find the equation of the horizontal asymptote, if it exists, for the following function. Justify your answer using a limit statement.

Evaluate the following limitalgebraically. You must show allwork to justify your answer.