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[DOC File]January 2006 - 6664 Core C2 - Question paper
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Find (a) the exact length of AB, (2) (b) the coordinates of the midpoint P of AB, (2) (c) an equation for the circle C. (3) 4. The first term of a geometric series is 120. The sum to infinity of the series is 480. (a) Show that the common ratio, r, is . (3) (b) Find, to 2 decimal places, the …
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[DOC File]New Chapter 3
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To find the area bounded by two curves we need to find the limits of integration. We do this by locating the points where the curves intersect. The definite integral for Figure 9.10 is represented by (Example 9.9 Find the area of the region bounded by and . (Solution First, we need to graph the two functions on the same coordinate plane.
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[DOC File]AP Calculus Free-Response Questions
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31. Given the curve x + xy + 2y2 = 6. a. Find an expression for the slope of the curve at any point (x,y) on the curve. b. Write an equation for the line tangent to the curve at the point (2,1). c. Find the coordinate of all other points on this curve with slope equal to the slope at (2,1). 32. a.
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[DOC File]MTH 254 - CALCULUS
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Be able to find the area enclosed by a curve given in polar coordinates. ( Be able to find the area enclosed between two curves given in polar coordinates. ( Be able to find the point(s) of intersection for two curves given in polar coordinates. ( Be able to find the length of a curve given in polar coordinates. 15.4 Double Integrals in Polar ...
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AREA UNDER A CURVE – NUMERICAL METHODS
Consider the curve , whose graph is given below: Suppose we want to find the area under the curve and above the x-axis, from to . So far, we have no tools to find an exact answer, so the best we can do is an approximation. To do this, we need to divide the region into rectangles and find …
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[DOC File]Primer On Integration
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Graph the function, and find the length of the curve from to . Solution. We use the equation . We have: So, Figure 7 Graph of the function Example 13. Find the area of the shaded region given in Figure 8. Figure 8 Graph of the function . Solution. For the sketch given, , and . Example 14
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C4 Mock - The Student Room
(ii) Find the exact value of . (5) 5. A curve is described by the equation . x3 ( 4y2 = 12xy. (a) Find the coordinates of the two points on the curve where x = –8. (3) (b) Find the gradient of the curve at each of these points. (6) 6. The points A and B have position vectors 2i + 6j – k and 3i + 4j + k respectively.
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[DOC File]Geometry name - Madison West High School
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Find the length of the curve , 2. Find the length of the curve , 3. Find the length of the curve , ... Compare the exact answer at x = 0.4 with the approximations found in (a) and (b). 10. Solve the differential equation . 11. Solve the differential equation . 12. Find the orthogonal trajectories of …
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[DOC File]Paper Reference(s)
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The curve has a maximum turning point A. (a) Using calculus, show that the x-coordinate of A is 2. (3) The region R, shown shaded in Figure 4, is bounded by the curve, the y-axis and the line from O to A, where O is the origin. (b) Using calculus, find the exact area of R. (8) June 2008. TOTAL FOR PAPER: 75 MARKS. END Question Number Scheme ...
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Find the exact length of curve