1. Which function has the greatest average rate of change on the interval 1 ≤ x ≤ 3? Show all your work! a. f(x) = 2x² b. g(x) = 3x² c. h(x) = -x²

Q: 2. S (2x-5)dx x2-5x+3

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Q: Using an appropriate substitution, the integral Jez-tan is equal to 2-tan sec²0 de O none of the…

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Q: - 1)n (n + 1)!) 3n!

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Q: The general solution of xdy - ydx = x²e*dx is A B с D y+xe*+cx=0 x-yex + cx=0 x+yex-cx=0 y−xe*-cx=0

A: We have to solve

Q: Suppose that f(x) = 6x + 3x². Evaluate each of the following: ƒ'(2)= f'(-1)=

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Q: 5. Krypton-85 is an inert radioactive noble gas with a half-life of approximately 10.76 years. a.…

A: Given half life of Krypton-85  is   t1/2=10.76 years

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent.…

A: We will apply Ratio-Test

Q: 6. Write down the partial differential equations for; (a) Diffusion equation (b) Wave equation,…

A: Diffusion equation identical to heat equation  Wave and Diffusion equation contains partial…

Q: The particular solution of (2x+3)y'=y+ (2x+3) ¹/2 ; y ( − 1) = 0 using LDE is A B C D -2y=√√2x +3 In…

A: Please see the below picture for detailed solution.

Q: A cargo container (in the shape of a rectangular solid) must have a volume of 520 cubic feet. The…

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Q: A linear function is given. A(r) = − 2/3 r − 6 (a) Sketch the graph.   (b) Find the slope of the…

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Q: The average value of a function f(x, y, z) over a solid region E is defined to be 1 = Favg VED ₁…

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Q: per distance between the bottom of the ladder and the wall? Oft/min O-4ft/min Oft/min 4ft/min…

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Q: An offshore oil well is 2 kilometers off the coast. The refinery is 3 kilometers down the coast (see…

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: Solution:

Q: The derivative of a function at each point is itself. y=kex

A: To find out the derivative of the function.

Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

A: Given points are,

Q: 2.) Sketch the region in the plane consisting of all points whose polar coordinates (r, 0) satisfy…

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Q: Using Integration by Parts, the integral [(x8. is equal to x10 5 - the above + 2x⁹) In x dx…

A: Given: I=∫x8+2x9lnxdx   Apply the integration by parts to solve the given integral. ∫udv=u·v-∫vdu

Q: ) ㅠ S tan5 (2x) sec² (2x) dx 2

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Q: Use the method of variation of parameters to determine the general solution of the given…

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Q: Verify the identity algebraically. Use a graphing utility to check your result graphically.…

A: Here, to simplify the expression: 7cos3(t)csc(t)

Q: For the equation given below, evaluate y' at the point (-2, 0). y - 6x² + 24 = 0.

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Q: Find the differential dy of the given function. y = In√√/9-x² dy =

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Q: 4) lim (1 + sin 4x)¹/x x→0+

A: Given limx→x+1+sin(4x)1x

Q: In the Midpoint Rule for triple integrals we use a triple Riemann sum to approximate a triple…

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Q: If k> 0 such that O St the above 4* dx = 3 then k = 2ln 2

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Q: 6. Use the difference quotient to estimate the 2 instantaneous rate of change in f(x) = x² at x=3…

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Q: Determine all the eigenvalues of the matrix G given below. Hence, obtain an eigenvector…

A: The understanding of Eigen value and Eigen vectors are required to solve these kinds of problems.

Q: Find the area of the region between the curve y = 1/1 + x^2 , 0 ≤x ≤√3, and the x-axis.

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Q: Find the radius of convergence, R, of the series. x4n n=2n(ln(n))² R = 8 Find the interval, I, of…

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Q: The derivative with respect to x of the function y = 3tan ¹x - y' = cotx O the above (In 3) log3…

A: Given y=3tan-1x-ln3log3cosecx

Q: Find the area of the region common to the interiors of the cardioids r= 1 - sin 0 and r= 1 + cos 0.…

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Q: Find dx 1 1 if y = 5x-3

A: Formula: d/dx 1/(ax+b) = -a/(ax+b)2

Q: Suppose the second derivative of a function f is f" (z) 0 (-∞, 1) U (1, 3) U (5,00) ○ (3,5) O (1,3)…

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Q: The measurement of the edge of a cube is measured to be 9 inches, with a possible error of 0.04…

A: We need to find out the possible error in the volume and also in the surface area and also the…

Q: 3 Solve the following GDES by variation of parameters method: 2X 니 ● ÿ - 4y + 4y = 12 ²X / X4 +10 2X…

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Q: Write a polar equation in rand of a hyperbola with the focus at the origin, with the eccentricity 2…

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Q: A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the…

A: We can solve as follows

Q: valuate the iterated integral below. π/4 1 St. + S² = 0 0 y cos (x) dy dx

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Q: 5. Determine the minimum and maximum values for y = 250(0.90)* for 0 ≤ x ≤ 6.

A: Given data y=2500.90x   To find maxima and minima we need to find critical points by equating dydx=0…

Q: d²x dt² (a) f(t) and h(t) are independent of t (b) f(t), h(t) and l(t) are independent of t (c) f(t)…

A: Solve the following

Q: In order to evaluate the following integral :-√2+√7 COS-¹ (v cos-¹(√x) dx we first use the…

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Q: N Given the series an, let SN=an be its Nth partial sum. Suppose that n=1 n=1 SN=8- A) Find a3. 5 N²…

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Q: Use a power series to approximate the definite integral, I, to six decimal places. 0.1 60⁰ I I = 1 1…

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Q: The total stopping distance T of a vehicle is shown below, where T is in feet and x is the speed in…

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Q: P7:TE %7 02 7 The derivative with respect to x of the function y=-3tan-¹x-(In 3) log; (csc x) is y'…

A: Given: y=3tan-1x-ln 3log3csc x

Q: ! The derivative with respect to x of the function sec y where y = sec ¹ (2* cot¹x) is sec(2* cot¯¹…

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Q: The derivative with respect to x of the function sec y where y sec¹(2* cot¹x) is

A: We can solve this as follows:

Q: Consider the following equations. f(x) = x5 + 3 g(x) = x + 3

A: Here we have to plot a graph.