Estimate the area between the x-axis and the graph of f(x) = 9-2² over the interval [-2, 1] by using the three rectangles shown here: 10+ e o 71 6- 5 4 3 2

Q: Compute limnon (√4n² +3-2n) and justify your calculations.

A: Introduction: In mathematics, the limit of a function is a fundamental concept in calculus and…

Q: Evaluate the definite integral. Le 1 t³ ln(3t)dt

A: Detailed solution is given below.   Integration by parts used here. ∫a(x)b(x) dx = a(x)∫b(x) dx -…

Q: Given a vector field F, div(curl( F )) will give a Ovector Oscalar value and has magnitude equal to

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Q: Graph the polynomial function f(x)= -2(x-2)(x²-25) using parts (a) through (e). (a) Determine the…

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Q: Which of the following improper integrals are finite and well-defined? (Tick all that apply) (A)…

A: The answer is in step 2.

Q: Find the point on the plane x - 2y + 3z = 9 that is closest to the point (0, 1, 2). (x, y, z) =

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Q: Suppose f(x)=√√3x + 9 and d g(x) = (fog)(x) = (gof)(x) = 1 7x-5

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Q: a lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline…

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Q: 4 Let u = (7,-3) and v = (4,8). Find O A. О в. O C. 19 5 OD. 12 44 (+) 5 . (8.12) D 5 1+ 3 -V.

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Q: Let a be a number and let f, g, and h be functions defined on on Interval I about a. Suppose that…

A: Given: limx→afx=7, limx→ahx=3 To find:  limx→2facosπx, limx→afxfxgx+3hx, limx→33-xx-3

Q: Use the product rule to find the derivative of the following. (Hint: Write the quantit as a…

A: By using the product rule to find the derivative of the following function. kt=t2-92

Q: Consider the following function on the region described by the inequality. f(x, y) = 2x² + 3y² -…

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Q: Question 9 Let The third component of v=3 and w w xv= [2] - 1 2

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Q: If D(p)=5400-60p and S(p) = 400+40p are demand and supply functions, respectively, find the…

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Q: or

A: We have to choose the correct option according to the given information

Q: Let a₁ = 1 2 a,₂ = and b= 4 - 20 h For what value(s) of h is b in the plane spanned by a, and a₂?…

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Q: Use the Ratio Test to determine if the following series converges absolutely or diverges. n²(n+2)!…

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Q: Find the limits in a) through c) below for the function f(x) = O A. a) Select the correct choice…

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Q: 8. For the curve given by r(t) = (sin³ t, cos³ t, sin² t), 0≤ t ≤, Find an equation for each (a) the…

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Q: 28 f. (7/₂) = x -J 12-x x-12 X+6 Olet fi R+R be defined as f(n)= 3√x + sinda and g: R-SR is defined…

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Q: Use integration by parts to evaluate the integral: S In(x) x7 - dx = Report your answer accurate to…

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Q: Use the alternative curvature formula k = r(t) = (5 cost,√2 sint, 3 cos t) |axv| to find the…

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Q: Find the trapezoidal Riemann sum approximation of √x² +3dx using four equal partitions.

A: This is a problem related to numerical integration. Please follow the procedure given below.

Q: Prove that there is some positive number such that 07 - 20+ sin(02+1) = √5. Your proof must quote…

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Q: Find c such that the function x ≤ c [x² - 8 10x 33 x>c f(x) = is continuous everywhere. C = с

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Q: Suppose f(x) = -5x - 10 and g(x)=√x²-3x +9. (fog)(x) = (fog)(5)=

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Q: Find the extreme values of f on the region described by the inequality. (If an answer does not…

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Q: Find f[g(x)] and g[f(x)]. f(x)=√√x+4, g(x)=12x² - 8 f[g(x)] = g[f(x)] =

A: Given query is to find indicated composite function.

Q: Find the limit 13 a) lim x-3 X+3 2 x 9 c) lim X->0 3-) 2 b) lim (6x² - 6 cos x) = 17² ? X->0 2 5 COS…

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Q: (-1)" n=0 6n

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Q: (a) (b) the direction at which the derivative of f(x, y, z)=2xy + yz at the poin P(1,-1,1) is -4. dy…

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Q: Using the Maclaurin series e = ∞ n=0 xn n! " ife find the general term of the Maclaurin series of…

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Q: Clear denominators in the following partial fraction decomposition and determine the constant B. 5x²…

A: Given;  (5x2+46x+73)/(x+8)(x+3)2= 1/(x+8) - B/(x+3)-4/(x+3)2

Q: Evaluate the integral. 8y' dy 8 y 8y' dy 8 y - 4 - 4

A: Solving the problem by finding the value of the integration.

Q: 2. Prove that there is some positive number such that 07-20+ sin(0² + 1) = √5. Your proof mus quote…

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Q: Find d dx d dx 2 8x² 3 8x² 3 7 2 5x² 7 2 5x =

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Q: Evaluate the integral: [V4 Ox= √4x² 2x² -dx (A) Which trig substitution is correct for this…

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Q: Determine the points at which the function f to the right has discontinuities. For each point state…

A: Condition of continuity1. fa is defined2. limx→afx exists3. limx→afx=fa

Q: Solve the initial value problem. d²y y = જર = 3-e²t, y(1) = -2, y'(1) = 4 ...

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Q: (c) A sequence (an)n-1 is recursively defined by (i) (ii) a₁ = √2 and an+1 = √√2+an for all n ≥ 1.…

A: Solve the following

Q: 사 In a certain year, the average e-mail user sent or received 157 e-mails each day. The number of…

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Q: Factor. 6v²-3-17v Select the correct choice below and, if necessary, fill in the answer box to…

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Q: It did not accept 824.77 as the answer

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Q: Find the derivative of the function: y=(8x-5)/(5x+6)   The derivative is y′=___________

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Q: lim [f(x) - g(x)] x→2 lim_[f(x) - g(x)]= [ X→2 (Simplify your answer.)

A: given limits are :-limx→2f(x) = 22 and      limx→2g(x)=8then we have to evaluate the following limit…

Q: Evaluate the integral. √3 [ arctan (1) dx 1

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Q: Find the absolute maximum and minimum values of f on the set D. f(x, y) = x + y - xy, D is the…

A: The given function:fx,y=x+y-xyThe closed region D is the closed triangle region with vertices 0,0,…

Q: A light is on the top of a 12 ft tall pole and a 5ft 6in tall person is walking toward the pole at a…

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Q: You know that: 16 •f f(t) dt = 31 0 ■ ■ f(4) = 21 f(16) = 25 - Evaluate: f(4 ln(x)) L I dx = Upload…

A: Given that ∫016f(t)dt=31, f(4)=21 and f(16)=25

Q: Evaluate the integral. 29 fe 9s √s ds ds =

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