# Difference between revisions of "009A Sample Final 2"

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== [[009A_Sample Final 2,_Problem_5|<span class="biglink"><span style="font-size:80%"> Problem 5 </span>]] == | == [[009A_Sample Final 2,_Problem_5|<span class="biglink"><span style="font-size:80%"> Problem 5 </span>]] == | ||

− | <span class="exam"> A lighthouse is located on a small island | + | <span class="exam"> A lighthouse is located on a small island 3 km away from the nearest point <math style="vertical-align: 0px">P</math> on a straight shoreline and its light makes 4 revolutions per minute. How fast is the beam of light moving along the shoreline on a point 1km away from <math style="vertical-align: 0px">P?</math> |

== [[009A_Sample Final 2,_Problem_6|<span class="biglink"><span style="font-size:80%"> Problem 6 </span>]] == | == [[009A_Sample Final 2,_Problem_6|<span class="biglink"><span style="font-size:80%"> Problem 6 </span>]] == |

## Latest revision as of 11:11, 25 May 2017

**This is a sample, and is meant to represent the material usually covered in Math 9A for the final. An actual test may or may not be similar.**

**Click on the** ** boxed problem numbers to go to a solution.**

## Problem 1

Compute

(a)

(b)

(c)

## Problem 2

Let

For what values of is continuous?

## Problem 3

Compute

(a)

(b)

(c)

## Problem 4

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

- at the point

## Problem 5

A lighthouse is located on a small island 3 km away from the nearest point on a straight shoreline and its light makes 4 revolutions per minute. How fast is the beam of light moving along the shoreline on a point 1km away from

## Problem 6

Find the absolute maximum and absolute minimum values of the function

on the interval

## Problem 7

Show that the equation has exactly one real root.

## Problem 8

Compute

(a)

(b)

(c)

## Problem 9

A plane begins its takeoff at 2:00pm on a 2500-mile flight. After 5.5 hours, the plane arrives at its destination. Give a precise mathematical reason using the mean value theorem to explain why there are at least two times during the flight when the speed of the plane is 400 miles per hour.

## Problem 10

Let

(a) Find all local maximum and local minimum values of find all intervals where is increasing and all intervals where is decreasing.

(b) Find all inflection points of the function find all intervals where the function is concave upward and all intervals where is concave downward.

(c) Find all horizontal asymptotes of the graph

(d) Sketch the graph of