Use Midpoint rule and Trapezoid rule as a pair to implement adaptive quadrature rule to approximate 4 dx o 1+x* with the tolerance of 10°. Show you resulting nodes on a real line.

Q: AX sex secX tan X

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Q: Analyze the graph of y = (arctan x)2.

A: Given- y=arctanx2 To Analyze- The above graph.

Q: y = arcsin (*) O find y" y" - V9 x2 None of the above O Option 2 y" = y %3D (9 – x2)3/2 (9 – x² )3/2…

A: Let's find.

Q: as the center of dilation. Point A(4, -9) is translated along the rule (x, y) - (x - 8. y+ 2). What…

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Q: all the a

A: The diagram is given in the problem is inscribed the quadrilateral in a circle . It is given that…

Q: When should they stop their engine so that they reach the space station? What is there position when…

A: We will use the fact that once engine is stopped the space craft will move along tangent to the path…

Q: Please draw the graph that shows the cross section of the function f(x,y)=2y^3+3y^2−2x+4 and the…

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Q: Use the Quadrature Rule Calculate I = S e2x dx using the 3-point Gaussian Quadrature method.

A: Given integral is I=∫03e2xdx

Q: Graph the curve and include the orientation: x(t) = t^3, y(t) = t+3

A: graph of above equation are as follows

Q: Can you clarify the first part again, does it mean that the relative maximum, minima, and horizontal…

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Q: Why was it not taken into account that the maximum distance between two points is a/3? and can you…

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Q: Find the length of the curve: - for 1< y<3. 3 4y 4. x=

A: As we know that the length of a curve x=f(y) is given by:- L=∫ab(f'(y))2+1dy

Q: Point M(-6,8) is dilated from the origin with a scale factor of 1/2. What is the coordinate of M'?

A: The idea of dilation is to make something bigger or smaller ( according to scale factor). Here the…

Q: a) For each pair of x-values below, in the figure above sketch the secant line through the corre-…

A: Note: The given question has multiple subparts, answer to the first three subparts are given. If…

Q: End the Vellue of g) if the slope of the Curve y= x-2x is (2)?

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Q: Trace the curve: r^2 = 4cos^4ꝋ tan^2ꝋ

A: The equation given in the question be, r2=4cos4θtan2θ Take square root on both sides implies,…

Q: A water tower has a right circular cylindrical tank oriented vertically with radius 3 m and height 6…

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Q: Find the distance from the point (1,–4,2) to the line x=2+t, y =-2+2t, z = 4 –t Try not to use any…

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Q: Estimate I = = I~|| +21 (8z + 82²)da using midpoints and n = 3 subintervals.

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Q: Determine the value of k which will make h' (7/4) = 6 when h(r) = ln (cos z) + kr. %3D O 5

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Q: find the points on the curve x^2+xy+y^2=16 which one nearest and farthest from the origin using…

A: Let us consider the given function f(x,y) Subjected to g(x,y)=C Solving using Lagrange's multipliers…