Calculus
1 Hour Exam 3 - Math
220 Fall, 2010
1. |
The function f(x) = 10 x3 – 20 x + 1 has one root in the interval [1,2]. In order to approximate this root, begin with an initial estimate of x1 = 2 and use Newton’s Method to obtain a second estimate x2. Write the value of x2 in decimal form. Answer: x2 = 1.59 |
2. |
Precisely state the Mean Value Theorem. |
3. |
A function f(x) has derivative f ‘ (x) = 6x2 + 5. Find a formula for f(x) given that its graph goes through the point (1, 15). Answer: f(x) = 2x3 + 5x + 8
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4. |
Evaluate the following limit. Be sure to use proper notation throughout your evaluation of this limit. n lim Σ [ 14k/n2 - 4/n ] k = 1 Answer: 3 |
5. |
The height of a tree is currently 100 inches. It is predicted that over the next 4 years The tree’s height will increase by 10 - 3√t inches per year where t represents the number of years from now. What will the tree’s height be 4 years from now? Simplify your answer. Answer: 124 inches
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6. |
Evaluate the following definite and indefinite integrals. π a. I = ∫ ( 8/x + 4 csc2 x + 3 ) dx b. I = ∫ ( 10 + 3 cos x ) dx π/2 2 c. I = ∫ (6x + 2 e-x ) dx d. I = ∫ x3 ( x4 + 7 )5 dx 0 e. I = ∫ sin3 x cos5 x dx f. I = ∫ ( 5 – 3 tan2 x) dx Answers: a. I = 8 ln x - 400 cot x + 3x + C b. I = 5π – 3 c. I = 14 – 2 e-2 d. I = (1/24) (x4 + 7) + C e. I = (1/4) sin4 x - (1/3) sin6 x + (1/8) sin8 x + C f. I = 8x – 3 tan x + C Click here to continue with this exam. |