A radar gun was used to record the speed of a runner during the first 5 seconds of a race (see table). Use Simpson's rule to estimate the distance the runner covered during those 5 seconds. t(s) 0 v (ft/s) 0.5 0 2.35 4.5 5 1 1.5 2 2.5 3 3.5 4 2.9 4.7 6.65 8.25 8.9 9.1 9.4 10.85 10.85

Q: 1) State the order of the given ordinary differential equation. Determine whether the equation is…

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Q: Find the horizontal and vertical asymptotes of f(x). 2x² f(x)= Find the horizontal asymptotes.…

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Q: Help determine the difference quotient and for f(x)=x^2+4

A: Given,. Difference quotient=

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A: To find the equation of a line parallel to y=−4x+4 and passing through the point (4, -21), you can…

Q: 4 Sª 3 16 (x-7)(x + 9) dx

A: I=∫3416(x−7)(x+9)dx

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Q: Give the partial fraction decomposition for the following expression. x² - 6x +29 2 X (x - 5)(x-1)(x…

A: we need to give partial fraction of

Q: ·b f(b) − ƒ(a) = f'(a)(b − a) – ſå ƒ''(x)(x − b)dx a

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Q: If z² = x² + y² with z > 0, dx/dt = 2, and dy/dt = 6, find dz/dt when x = 6 and y = 8. dz dt Answer:…

A: The Power Rule:The Chain Rule:

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A: The populations of Towns A, B, and C vary exponentially with respect to time.1.The population of…

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Q: 6. Given f(x) = 3x - 1 A. Find (f-g)(x) B. Find (fog)(x) report domain and simplify C. Find (3) (2)…

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Q: Let f (x) = - x² – 3. Find and simplify ƒ' (x) and ƒ" (x). x5 f" f'(x) = A = -3 B C = || f" (x) D E…

A: Given Function f( x ) as follows

Q: 12. {yly = x² - 1, x = integers}

A: {y/y=x2−1,x∈integer}

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Q: Use the Table of Integrals to evaluate the integral. e √e2x 1 dx =

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Q: Find aw/as and aw/ât using the appropriate Chain Rule. Function Values w = y³ - 2x²y x = es, y = et…

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Q: 4. For each integer n ≥ 0, define In = [cos" (a) da. (a) Use integration by parts to prove the…

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Q: Given C = x³ – 6x² + 9x +4 13 a) Find C'(x) = Find any critical values of C'(x) b)x= Use interval…

A: Given,

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Q: Find the area of the shaded region. -1.0 -0.5 y 8 6 y=3e 4 2 0.5 (1, 3e) y=3xet² 1.0 1.5 2.0 X +

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Q: Use the Gauss-Seidel iterative method to solve the following system of equations. Remember to show…

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Q: The diagram below shows upper and lower sums for the function f(x)=√√x+1 using 4 subintervals. Use…

A: given function

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Q: (a) Find the unit tangent vector on the curve r(t) = [cos(t),2t, 3sin(4t)] when t = 0. :

A: To find the unit tangent vector on the curve .Note: Since the student has posted multiple questions…

Q: 5. Let f(x, y, z) = x²e + ay³ + az + 115. Find fyzz (b) Find 8³1 əxəydy'

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Q: y-values 9 8- 7 6 5- * 3 2 1 If f(x) f'(3) = g(x) 1 g(x) h(x) > 2 3 x-values then 4 y-values 4 3 2 1…

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Q: J 4³ (u + 1)² du

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Q: To test this series for convergence ∞ n=1 n n6 + 7 You could use the Limit Comparison Test,…

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Q: X 0 1 f(x) 3 2 f'(x) -2 -1 2 X g(x) g'(x) 2 1 2 0 1 2 1 3 5 3 -2 324 320 4 3 4 1 0 4 5 -1 0 4 اس 54…

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Q: Evaluate the limit: limħ– →0 0-2 01/1/20 0 - 12/1/2 2 an ( 7 +h)-tan (7) h

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Q: Find the reduced echelon form of the matrix: M 1 2 3 1 4 1 2 19

A: The Matrix is given by :

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Q: x³ (4x - 4)5 Let f(x) = 3x² - 3 If we use the method of logarithmic differentiation to find f'(x),…

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Q: Consider g(z) = -10z + 15z² - 9 Determine the intervals on which g is concave down. g is concave…

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 2t²1 - 4tj + (a) r(t) (b) r"(t) (c)…

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Q: Use the parametric curve, and given value for the parameter, to answer the following question. Use…

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Q: Evaluate the integral. Answer= +C -22e-30 e2x + 6e +5 12276 -da

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Q: Find the general solution of the ODE: y' y²-6y+10 = 1 =

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Q: (b) Suppose that f(x) = 2x^2 − x^4 . Find the intervals on which f is increasing and those on which…

A: Question no. (b):Suppose that To find the intervals on which is increasing and those on which it is…

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Q: For which values of x are the vectors (2x, 4, x) and (-1, -2, x) orthogonal? Select one: O-4 and 2…

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Q: Evaluate the following integral 6x + SS (8x - y) In (8x - y) dA R where R is the region bounded by…

A: Given that, where R is the region bounded by the graphs of                  Using the change of…

Q: (a) Find the unit tangent vector on the curve r(t) = [cos(t),2t, 3sin(4t)] when t = 0. (b) Evaluate…

A: Given curve:Unit tangent vector is given by,Therefore,