Approximating a Function The table lists several measurements gathered in an experiment to approximate an unknown continuous function
x | 0.00 | 0.25 | 0.50 | 0.75 | 1.00 |
Y | 4.32 | 4.36 | 4.58 | 5.79 | 6.14 |
x | 1.25 | 1.50 | 1.75 | 2.00 |
y | 7.25 | 7.64 | 8.08 | 8.14 |
Approximate the
Using the Trapezoidal Rule and Simplson’s Rule.
Use a graphing utility to find a model of the form
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Chapter 8 Solutions
Calculus (MindTap Course List)
- Find the area of the region. f(x) = x-3/x The x y-coordinate plane is given. There is 1 curve and a shaded region on the graph. The curve starts at x = 3 on the x-axis, goes up and right becoming less steep, and ends at the approximate point (5, 0.40). The region below the curve, above the x-axis, and between 3 and 5 on the x-axis is shaded.arrow_forwardBasic Intergration Rules Evaluate the following integrals. Check by differentiation. ∫ ( 6 x^3 − 4 x + 1 ) d xarrow_forwardWaiting for the Train. A commuter train arrives punctually at a station every half hour. Each morning, a commuter named John leaves his house and casually strolls to the train station. The time, in minutes, that John waits for the train is a variable with density curve y = 1/30 for 0< x< 30, and y = 0 otherwise. a. Graph the density curve of this variable. b.. Show that the area under this density curve to the left of any number x between 0 and 30 equals x30. What percentage of the time does John wait for the train c. less than 5 minutes? d. between 10 and 15 minutes? e. at least 20 minutes?arrow_forward
- The area bounded by the functions f(x) equals X^3 And g(x) equals X , and the lines X equals 0 and x equals one. find or approximate to two decimal places the described areaarrow_forwardWaiting for the Train. A commuter train arrives punctually at a station every half hour. Each morning, a commuter named John leaves his house and casually strolls to the train station. The time, in minutes, that John waits for the train is a variable with density curve y = 1/30 for 0< x< 30, and y = 0 otherwise. a. Graph the density curve of this variable.b. Show that the area under this density curve to the left of any number x between 0 and 30 equals x/30. What percentage of the time does John wait for the trainc. less than 5 minutes?d. between 10 and 15 minutes?e. at least 20 minutes?arrow_forwardIntegrating over general regions: Evaluate the double integral. ⌠⌠ (x^2 +2y) dA D is bounded by y = x, y = x3, x ≥ 0 ⌡⌡Darrow_forward
- Integral Calculus Area under the Curve 1. What is the area of the region bounded by y=2^x and the lines x=1 , x= -1 and y=0?arrow_forwardApproximating the displacement Suppose the velocity in m/s of an objectmoving along a line is given by the function v = t2, where 0 ≤ t ≤ 8. Approximate the displacement of the object by dividing the time interval [0, 8] into n subintervals of equal length. On each subinterval, approximate the velocity with a constant equal to the value of v evaluated at the midpoint of the subinterval.Divide [0, 8] into n = 4 subintervals: [0, 2], [2, 4], [4, 6], and [6, 8].arrow_forwardAn unknown constant Let a. Determine the value of a for which g is continuous from theleft at 1.b. Determine the value of a for which g is continuous from theright at 1.c. Is there a value of a for which g is continuous at 1? Explain.arrow_forward
- Regions of integration Write an iterated integral of a continuous function ƒ over the region R. Use the order dy dx. Start by sketching the region of integration if it is not supplied. R is the region in the first quadrant bounded by the x-axis, the linex = 6 - y, and the curve y = √x.arrow_forwardApproximating the displacement Suppose the velocity in m/s of an objectmoving along a line is given by the function v = t2, where 0 ≤ t ≤ 8. Approximate the displacement of the object by dividing the time interval [0, 8] into n subintervals of equal length. On each subinterval, approximate the velocity with a constant equal to the value of v evaluated at the midpoint of the subinterval.Divide [0, 8] into n = 8 subintervals of equal length.arrow_forwardBasic Intergration Rules Evaluate the following integrals. Check by differentiation. ∫ ( √x − 1/√x ) d x Show step by step and what rule did you used.arrow_forward
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