Welcome to the Jeopardy of Calculus AB The
Welcome to the Jeopardy of Calculus AB. The questions are based on Chapter 4 Materials. Let’s go to the Game Board
Categories Area Integration Mental Funds U-Substitution Potpourri $ 100 $ 100 $ 200 $ 200 $ 300 $ 300 $ 400 $ 400 $ 500 $ 500 Final Jeopardy
Area 100 Find the sum. Answer
Answer The distributive property of summation says that we can place any constant outside of the sigma notation. = Categories
Area 200 Find the sum. Answer
Answer We evaluate this sum by replacing k with 0, then 1, 2, 3, and 4 respectively. Categories
Daily Double!!! • Choose the amount you would like to wager. (Up to half your score) Question
Area 300 Find a formula for the sum of n terms. Use the formula to find the limit as n infinity. Answer
Answer Evaluate the summation: After simplifications: And the answer: Categories
Area 400 Determine a value that best approximates the area of the x-axis and the graph of the function over the indicated interval. f(x)= 4 – Answer 2, x [ 0, 2]
Answer First sketch a graph of the function: Then approximate counting the squares: A=1+1+0. 5+0. 5=5. 5 Categories
Area 500 Find the sum: Answer
Answer Solve the summation: Categories
Integration 100 Answer
Answer Integrate each part separately. Don’t forget the C! Then rewrite to: Categories
Integration 200 Answer
Answer Integrate Categories
Integration 300 Answer
Answer First, integrate t 2 separately from –sint. Then integrate –sint. (Chain Rule) Then rewrite to: Categories
Integration 400 Solve the differential equation: Answer
Answer First, integrate the equation. Then plug in 2 for x, and find C. Then rewrite to: Categories
Integration 500 Calculate the indefinite integral: Answer
Answer First divide the entire equation by the x in the denominator. Then integrate each piece independently of each other. Categories
Mental Funds 100 Find the area of the region bounded by the equation: On the interval [0, 2]. Answer
Answer Categories
![Mental Funds 200 Find the average value of: On the interval [1, 4]. Answer](http://slidetodoc.com/presentation_image_h/fcfd0dd1ee84a4f8bcb494711d56913b/image-27.jpg "Mental Funds 200 Find the average value of: On the interval [1, 4]. Answer")
Mental Funds 200 Find the average value of: On the interval [1, 4]. Answer
Answer = Categories
Mental Funds 300 Evaluate the definite integral: Answer
Answer First Expand: Then Integrate: Then plug in the Numbers: Answer: Categories
Mental Funds 400 Using the second fundamental theorem of Calculus find F’(x): Answer
Answer Simply plug in x for t. Categories
Mental Funds 500 Using the second fundamental theorem of Calculus find F’(X) Answer
Answer Using chain rule derive the inside and then plug in the 3 x. Categories
U-Substitution 100 Answer
Answer Thus: u = 2 x; du = 2 dx; ½du = dx ½(cosu) ½cos 2 x Categories
U-Substitution 200 Answer
Answer U = x 2+1; du = 2 x dx; ½du = x dx ½ =½ Categories
U-Substitution 300 Answer
Answer Categories
U-Substitution 400 Answer
Answer Categories
U-Substitution 500 Answer
Answer Categories
Potpourri 100 Derive: Answer
Answer Categories
Potpourri 200 Find the limit: Answer
Answer You should know that as x approaches 0 in the limit: The limit equals one. Categories
Potpourri 300 Derive this equation: Answer
Answer Categories
Potpourri 400 Integrate: Answer
Answer Categories
Potpourri 500 Integrate the indefinite Integral: Answer
Answer Expand: Integrate: Answer: Categories
Final Jeopardy • Think about your wager for final Jeopardy!
• The category is: The Angle between two Vectors!
• Just Kidding! • Your Category is: Area Approximations!
Decide wager amount Wager some, all, or nothing…
Use Trapezoid Rule to Approximate: n=4
Solution:
![Solution: We now use Trapezoid Rule to approximate the definite integral. Answer: [2. 0599]](http://slidetodoc.com/presentation_image_h/fcfd0dd1ee84a4f8bcb494711d56913b/image-61.jpg "Solution: We now use Trapezoid Rule to approximate the definite integral. Answer: [2. 0599]")
Solution: We now use Trapezoid Rule to approximate the definite integral. Answer: [2. 0599]
Area! • Using integration, and arithmetic sums, to determine the area produced between the graph and the x-axis. Categories
Integration! • Using basic integration to determine both definite and indefinite integrals. Don’t forget the + C! Categories
Mental Funds! • Understand the fundamental theorems of calculus for this part…you’ll need them. TRUST ME! Categories
U-Sub! • Using U-Substitution, find the integrals of some problems. • Warning…some of these problems are rather difficult! Categories
Potpourri! • Anything and Everything From the Three Previous Chapters! HAHA! • Solvers Beware! Categories
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