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Calculus (MAT-251)     Graded Exam  1     2.1     2.2     2.3     3.1     3.2     4.1    4.2       Midterm   1    2     Final Exam  1   2            
Lesson   1    2    3    4    5    6    7    8    9    10    11    12    13    14    15    16    17    18    19
Calculus I (MAT-251)
Graded Exam 3a
There is a hill which has parallel train tracks on it. The tracks run for 6 miles up the hillside.
One train is at the top of the hill, moving down at 19 mi /h. Another train is on the other set of tracks,
moving up the hill at 10 mi /h. The first train accelerates at 10 mi /h as it goes down the hill,
but the second train does not accelerate or decelerate. How far up the hill are they when they pass?
 
            Answer:     2 mi
 
Explanation:


 
Evaluate the indefinite integral
 
                        Answer:    ln |1 – x2| + C
 


 Explanation:


 
Evaluate the indefinite integral  dt.
 
                        Answer:   
 
Explanation:


 
True or false?
When using rectangles to estimate the area under a curve,
all the rectangles must have the same width.
 
                        Answer:     False
 
 
Evaluate 
 
                        Answer:     1
 
Explanation
Plug   into x
 Simplify (sin x cancels out ln), subtract ( )

                                                                                                    = 1
 

I am stuck in Austin with a flat tire, and I need to get to my class in Houston within 2 hours.
The drive is 180 miles long, but I want to be careful of the Austin cops.
I do not usually get caught speeding unless I am seen accelerating too fast, so I do not want to
accelerate at a rate of more than 120mi/h. Just to be careful, I′m going to take exactly 2 hours
to make the trip. Assuming I accelerate at 120 mi/h for a while, and travel at a constant speed
afterwards, what’s the fastest speed I′ll be going during my trip
 
                        Answer =     120 / h
 
Explanation
 
 
Evaluate the indefinite integral:
                                                               

                      Answer:  
 
Explanation





Suppose you dig a hole 52 feet deep and place a baseball machine in the hole,
so that the balls fire out at 96 ft/s and land on the ground outside the hole.
What is the velocity of one of these baseballs when it hits the ground?

 
             ft/s

 
Explanation
-96 · 96 – 2 · –32 · 52 = 76.58
-16√23 = 76.58
 
What is the area between the curves y = cos x + 3 and y = sin x -1 from x = -tt to x = 3tt
What is the area between the curves x = y2 – 9 and x = -y2 + 9
 
            Answer: 72


Explanation:
x = y2 – 9 and x = -y2 + 9
y2 – 9 = -y2 + 9 =
2y2 = (3, -3)
2(3 + 3)2 = 2(6)2 = 72
 
Evaluate the indefinite integral    .
 
                
 
 
Explanation
 

Calculus (MAT-251)     Graded Exam  1     2.1     2.2     2.3     3.1     3.2     4.1    4.2       Midterm   1    2     Final Exam  1   2            
Lesson   1    2    3    4    5    6    7    8    9    10    11    12    13    14    15    16    17    18    19     Need Homework Help?      Need A Tutor?
What is the area beneath the curve     y = x3 + 3x + 3 and the x-axis from x = 0 to x = 2


                   Answer: 16
 
Explanation
Rewrite the equation like so.




Evaluate the indefinite integral:
 
            

                       
 Explanation


 
Evaluate the indefinite integral:
                                                          
 
            




Explanation


Evaluate the indefinite integral: 
                                                        

 
                     Answer: x ln 2 + C  
 


Evaluate
                  

                                    Answer:     0
 
Explanation
Since its numerator approaches a real number while its denominator is unbounded,
the fraction 1/ln(x) approaches 0.
 
 
Evaluate
                    
 
            
                                                                           Answer:     1
 

Explanation








What is the area beneath the curve g(x) = ex + 2x + cos x from x =  to x = 2 ?
 
                        Answer: e2π- e π + 3π2
 
Explanation
Write the equation then find the integral.


 
 Evaluate:       
 
                       
                                               Answer: 1/2
 
Explanation







 Evaluate:
                

                        Answer: -2

 
Explanation



What is the area of the triangle bounded by the lines:     x = 1, y = x - 1, and y = 3 - x?
 
                    Answer:     1
 
Explanation
We write the integral equation and evaluate.


Calculus (MAT-251)     Graded Exam  1     2.1     2.2     2.3     3.1     3.2     4.1    4.2       Midterm   1    2     Final Exam  1   2            
Lesson   1    2    3    4    5    6    7    8    9    10    11    12    13    14    15    16    17    18    19     Need Homework Help?      Need A Tutor?

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