Find the area of the given region. Use a graphing utility to verify your result. y = 1 + In x³ X y 1 -1 2 3

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Q: 22) Determine the value of f(t)dt given that £15 f(t)dt = -10 and 5,5 f(t)dt = 9.

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Q: v = {3,k,-2} and w = {-2,1,2k} What value(s) of k are the vectors v and w perpendicular?

A: To determine the value of k for which the vectors v and w are perpendicular.v=3, k, -2 and w=-2, 1,…

Q: Find the area of the region bounded by the graphs of the algebraic functions. f(x)=x² +34x+289 g(x)…

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Q: Determine the solution of the following differential equations. a) (D² +9) y = 81x² + 14cos3x

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Q: EC: Find the derivative of g(x) (x) = = 0 cos(t²) dt cos(1¹) di

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Q: 10) Does the sequence an = √n² + 3n - n converge or diverge? Explain

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Q: 3) Solve the differential equaion (D2-4)y=e²-4

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Q: Use Stokes' Theorem to find the circulation of F = 4y? +7zj + 7xk around the boundary of the surface…

A: According to question,Given vector,F→ = 4yi→ + 7zj→ + 7xk→z = 64-x2 + y2for z≥0.

Q: Given the absolute function graphed below, find the following: a) Domain: -12 Decreasing: 6 5 4 7 2…

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Q: (6417 #3 p. 357) Find the average value of f(x) = 6r-r² f(x= on the interval 2<z≤8

A: Given function is f(x)=6x-x2 and the interval is 2≤x≤8.

Q: ) If we would like to solve the following differential equation by variation of parameters 3x then…

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A: Here is the solution:

Q: Identify the circle that has center (6,-3) and radius 3. Select the correct answer below: O (x+3)² +…

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Q: (b) n=1 3 2n-1

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Q: es for the point (4, IN

A: given (r,θ)=(4,2π3)formula for other coordinates is  (r,θ+2nπ) or  (-r,θ+(2n+1)π)

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A: Given query is to simplify the expression.

Q: → R be a function defined by 3x² + x+5 f(x) = not continuous at x = = 0.

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Q: 4) Evaluate 2 √x√x² +1 dx

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Q: 27) Suppose y = f(x) and y = g(x) are continuous functions which intersect at x = 1, x = 4 and x = 7…

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Q: ble answers No Answers Chosen The range is all real numbers. ous The equation of the asymptote is x=…

A: We will find the required.

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Q: Find the average value of f on [0, 8]. YA 1 0 2 4 6 X

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Q: d) xy' + (1+x)y=e* sin(2x)

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Q: The region between the curve y = √x, 0 ≤ x ≤ 4, and the x-axis is revolved about the x-axis to…

A: Given y = x0 ≤ x ≤ 4 as we know that volume pf solid bounded by revolution of y = f( x ) V =…

Q: Sketch the region R and compute ff 2xdxdy, where R is the region bounded by x = y² and (x-1)² + y² =…

A: To find:- ∬R2xdxdy Where R is the region bounded by x=y2, x-12+y2=1

Q: Find the length of the loop of the given curve. x = 6t - 2t³, y = 6t²

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Q: 19. lim x²-5x-24 x-5 x²-9

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Q: 2. Find y' using implicit differentiation where x² + 4y² = 4

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Q: Which of the following represents the series? −13 + (−7) + (−1) + 5 + 11      b    c    d

A: given  series is  -13+(-7)+(-1)+5+11first term is   -13

Q: If f(8) = 2, write an ordered pair that must be on the graph of y f(x - 11) + 4.

A: Given data, f8=2 and y=x-11+4

Q: Differentiate the function. g(t) = 9t + 8t² g'(t) = 9+16x X

A: given  g(t)=9t+8t2we know  dtndt=ntn-1g'(t)=d(g(t))dt

Q: 2 Find the area between the graph of y = 5 – 5x³ and x-axis and − 1 ≤ x ≤ 8 using properties of…

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Q: Let F(s) = L-¹{F(s)} = ? 1 f(t) = e-8 tsin(√7t) √7 f(t)=e8tsin(√7t) O O f(t) = e 1 s²+16 s+71 -8 t…

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Q: Let C be the curve f(x) = the length of C, as follows: (1) Calculate f'(x). In(x) 2 - 4 between 1…

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Q: Evaluate the integral 25 (28-4) ¹3 dz 13 x6 - 4. by making the substitution u = x + C

A: SOLUTION-

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Q: For a given commodity and pure competition, the number of units produced and the price per unit are…

A: Let's find consumer surplus and producer surplus.

Q: 2) Consider the function: f(t) = 0, e-kt, 0 ≤ t < 1 1 ≤t. A) Use the definition to find F(s) =…

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