# If it is false explain why or give an example that

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Chapter 3 / Exercise 1
Invitation to Computer Science
Gersting/Schneider Expert Verified
If it is false, explain why or give an example that disproves the statement. 1. If and are continuous on , then 2. If and are continuous on , then 3. If is continuous on , then 4. If is continuous on , then 5. If is continuous on and , then y b a s f x dx y b a f x dx f x 0 a , b f y b a xf x dx x y b a f x dx a , b f y b a 5 f x dx 5 y b a f x dx a , b f y b a f x t x dx y b a f x dx y b a t x dx a , b t f y b a f x t x dx y b a f x dx y b a t x dx a , b t f 6. If is continuous on , then . 7. If and are continuous and for , then 8. If and are differentiable and for , then for . 9. 10. 11. 12. represents the area under the curve from 0 to 2. 13. All continuous functions have derivatives. 14. All continuous functions have antiderivatives. y x x 3 x 2 0 x x 3 dx y 1 2 1 x 4 dx 3 8 y 5 5 ax 2 bx c dx 2 y 5 0 ax 2 c dx y 1 1 x 5 6 x 9 sin x 1 x 4 2 dx 0 a x b f x t x a x b f x t x t f y b a f x dx y b a t x dx a x b f x t x t f y 3 1 f v d v f 3 f 1 1, 3 f |||| 5 Review C O N C E P T C H E C K 1. (a)Write an expression for a Riemann sum of a function .Explain the meaning of the notation that you use. (b) If , what is the geometric interpretation of a Riemann sum? Illustrate with a diagram. (c) If takes on both positive and negative values, what is the geometric interpretation of a Riemann sum? Illustrate with a diagram. 2. (a) Write the definition of the definite integral of a continuous function from to . (b) What is the geometric interpretation of if ? (c) What is the geometric interpretation of if takes on both positive and negative values? Illustrate with a diagram. 3. State both parts of the Fundamental Theorem of Calculus. 4. (a) State the Net Change Theorem. f x x b a f x dx f x 0 x b a f x dx b a f x f x 0 f (b) If is the rate at which water flows into a reservoir, what does represent? 5. Suppose a particle moves back and forth along a straight line with velocity , measured in feet per second, and accelera- tion . (a) What is the meaning of ? (b) What is the meaning of ? (c) What is the meaning of ? 6. (a)Explain the meaning of the indefinite integral . (b) What is the connection between the definite integral and the indefinite integral ? 7. Explain exactly what is meant by the statement that “differen-tiation and integration are inverse processes.” 8.State the Substitution Rule. In practice, how do you use it?
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The document you are viewing contains questions related to this textbook. The document you are viewing contains questions related to this textbook.
Chapter 3 / Exercise 1
Invitation to Computer Science
Gersting/Schneider Expert Verified
1. Use the given graph of to find the Riemann sum with six subintervals. Take the sample points to be (a) left endpoints and (b) midpoints. In each case draw a diagram and explain what the Riemann sum represents.
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