Calculate the derivative. (Use symbolic notation and fractions where needed.) r cos(s) u du = ds J

Q: Find a general term (as a function of the variable n) for the sequence {a1, a2, az, a4, ...} =…

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Q: lim レ+x- %3D X. x→0 e-X+1 x -x_ a Find the limit.

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Q: Find the power Series and determmine the radius of convergence. f()= X x'+16 representation for Hhe…

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Q: Solve the following differential equations of 1– y' = 2y – x; 2-x'y'y'+

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Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 3 + 4x3/2…

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Q: Find the Fourier series expansion of the periodic ʻramp' function f(x)= 2x, valid between x = 0 and…

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Q: An animal population N(t) is modeled by the differential equation = 0.00005N (N – 200).If N(0)=A,…

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Q: Use the Limit Comparison Test to determine the convergence or divergence of the series. Σ n V n2 + 4…

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Q: Suppose y(t) = 4e-5t is a solution of the initial value problem y' + ky = 0, y(0) = yo. What are the…

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Q: Use the Comparison Test to determine whether the series is convergent or divergent. 1 n3/4 n- 2 Σ -…

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Q: a) Find the average value of the function f(x)= 1+4x-3x? on the interval [0, 2]. Average Value= b)…

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Q: dy х+3у. dx 2х

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Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

A: Use derivative and critical point for finding the absolute maxima .

Q: Determine if B is the inverse matrix of A. 1 01 - 2 1 1 A = 2 1 3 В - - 5 2 - 1 -1 1 1 3 - 1 1 Is B…

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Q: Determine the length of x =(y – 1)3/2 between 1<y< 4.

A: We can determine the length of the curve as below.

Q: Which of the following is equal to ſ e®dt? А. ее В. ее + С С. ееx + С D. eet + C

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Q: Find the point of diminishing returns (x,y) for the function R(x), where R(x) represents revenue (in…

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Q: Not yet answered Question 1 Marked out of 1.00 c3 m³+1 dx Evaluate: x 3 a 16.664 2 16.635 2 12.654 2…

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Q: Determine the volume of the solid generated by revolving the region bounded by y = x2 – 4x + 5, the…

A: The given curves are; y=x2-4x+5, x=1, x=4, y=0 x-axis From the given curves the bounded region is as…

Q: The population A (in thousands) of Atlantic City in 2014 was 39,521. In 2018, the population was…

A: The population A in thousands of Atlantic City in 2014 was 39,521. In 2018, the population was…

Q: Find the number of 3-permutations of a set with seven elements. a. 130 b. 120 c. 210 d. 100

A: Let's find.

Q: Express as a single logarithm. A) log 5 + log 11

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Q: Find f. f'(x) = 6x – 3/x*, x > 0, f(1) = 7 f(x) =

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Q: Consider the following function. f(x) = -7x + 21x + 2 (a) Find the critical numbers of f. (Enter…

A: The given function,      fx=-7x3+21x+2

Q: Evaluate the integral. 2. Se 3x dx 0.

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize…

A: Maximize f(x,y)=4x+4xy+y Constraint: 4x+y=200.

Q: Find the area of region A in Figure 6. F FIGURE 6 F:r= 18 cos 0, G:r 1 ry = 1, r = 9 Answer:…

A: Solve for area. (Using integration we can find the answer.)

Q: Find the area of the region bounded by y = 6x-x? y=2x

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Q: Find the power Series representation for the function land determine the radlius of convergence.…

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Q: Find the intervals on which the graph of f is concave upward, the intervals on which the graph off…

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Q: Consider the function whose graph is the surface shown at the right. Which traces go with which…

A: y=-1.9 C x=1.9 E y=-0.5 F x=-1.9 D

Q: On a sketch of y= e*, represent the left Riemann sum with n = 2 approximating ff e dx. Write out the…

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Q: 7. Given y =x*in*, calculate y'. sinx sinx A) y'=xin* (sin.x Inx + cos x Inx) C) y'=x*inx + cos x…

A: For the solution of the problem follow the next step.

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 – 2xy + y?,…

A: Solving tangent equation

Q: Consider the the curve y =(6x + 5)V6x + 5 from x =5 to x 11 a) Find the initial and terminal points:…

A: Consider the curve y=6x+56x+5 from x=5 to x=11.a To find the initial and terminal points.b To find…

Q: cos*x _8. If S(cos³x · B) dx = A. -sin x + C, what is the B? С. cos x D. secx B. csc x

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Q: Use the Limit Comparison Test to determine the convergence or divergence of the series. V n8 + 5 n=…

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Q: Let f(x) = 4x + 3, g(x) = −2x2 + 4. a) Find the average rate of change of g(x) from 0 to 2. b) Find…

A: a) Average rate of change of a function over an interval [0,2] is given by A=g(b)-g(a)b-a Given,…

Q: V9x2+4 dx V9x2+4 +c V9x2+4 +c 3

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Q: Solve the problem. Determine the dimensions of the rectangle of largest area that can be inscribed…

A: From the figure:Let 2x be the length of the rectangle;Hence,using Pythagoras theorem;width2+2x22…

Q: : Find the volume of the solid obtained by rotating the region bounded by the curve y= -x²+ 10 and y…

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Q: Find det A using the method of cofactors and the sign matrix. 2 2 6 A = 0-8 6 - 2 0 1 det A =…

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Q: So, the volume of the solid of revolution is Volume = V = TI (9 - x2)2 dx. To find the volume,…

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Q: _1. There is no function f(x) such that S f(x) = f (x) + C.

A: To determine whether the given statement is True or False.There is no function fx such that ∫fx…

Q: Determine whether or not the improper integral is convergent, and find its exact value if it is…

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Q: Katie invested an amount of $18,000.00 in a mutual fund. After 4 years and 6 months the accumulated…

A: Use the formula for the compound interest and calculate the rate.

Q: sinx 18. Supposed Ax) = [ V1+t* dt and g(y) = | f(x)dx , what is the value of g' 15 A) 2 C) B) D)

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Q: Show that the production function f(x) = - () x³ + 10x² + 5x, –∞<x<∞ has both a concave and convex…

A: Second derivative shows the concavity of any curve.

Q: A particle travels along the x-axis such that its position is given by a(t) = (t0.9 – 3t) cos (2t).…

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Q: Find the direction in which the function is increasing most rapidly at the point P0. f(x, y, z) = xy…

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