Use the midpoint approximation to approximate the area under the curve of f(x) = + +2 on the interval [-4, 2] using n = 6 rectangles. 10 F Submit your answer using an exact value. For instance, if your answer is then enter this fraction as your answer in the response box. 3 Provide your answer below: M Area unit²

Q: Let y = 3x² + 3x + 4. ind the differential dy when x = 4 and dx = 0.4 ind the differential dy when x…

A: Given query is to find differential at given point.

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Q: find ℒ{f(t)}. (Write your answer as a function of s.) f(t) = (t + 1)3 ℒ{f(t)} =

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Q: Let y = tan(5x + 2). Find the differential dy when x = 2 and dx = Find the differential dy when x =…

A: We have to find out the differential

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Q: Let y 3x² + 3x + 4. = Find the differential dy when x = 4 and dx = Find the differential dy when x =…

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Q: uestion you were to use a substitution of u = cos(x) to evaluate the definite integral below, what…

A: We have to find the integral

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Q: Q4/Find x and y that make the equations equal to zero: 5x+2y-4-0 6x+8y-2-0

A: Simplify both equation for x and y .

Q: Homework Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule.…

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Q: Let y 5x²8x + 4. If Ax = 0.1 at x = 1, use = differentials to estimate Ay Δy ~

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Q: 7- dx L₁EV xV1 + (In x)²

A: Here we will use the substitution method

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Q: 4. Find the limit, if it exists. If the limit does not exist, explain why. √3x²+4-4 (a) lim x-2x²…

A: a) limx→23x2+4-4x2-x-2b) limx→326x2-11x+38x3-27

Q: (2) Evaluate the iterated integral by converting to polar coordinates. 1 √x-x² (x² + y²) dx dy [] 0…

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Q: 4. (a) Find the general form of the equation of a line through A (2,-2) and B (-2,3). 4. a) (b) Use…

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Q: Evaluate the following integrals I 1. x² - x 1+3x²2x³ dx J₁ 2. /1+2 I dx 1 + 2 sin r ²+2 3. da x + 1…

A: Note that, according to Bartleby guidelines, we can answer only the first 3 sub-parts in the case of…

Q: Find the value for k so that the function will be continuous at x = -4. f(x) = 7x + 47 -x² + 18x81+k…

A: Topic = Functions

Q: Find the average value gave of the function g on the given interval. TU TU g(x) = 6 cos(x), 2 2 gave…

A: We will find the average value of function as shown below

Q: 1- 2- 3- 3-Evaluate the integrals in Exercises: [ sect? (x - 1) dx sech² s sech Vt tanh Vt dt Vt…

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Q: 10z Sketch the region enclosed by y = 5, y = el, and a = 1. Find the area of the region.

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Q: Consider the following function: f(x) = - -x4 + 2x³ +6 Step 2 of 4: Determine where the function is…

A: Here is the solution:

Q: he vector, parametric, and scalar equations of the plane for each of g situations: 1961 301 il bari…

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Q: 1. Consider the curve y = f(x) = 2* - 1. A. Find the exact area of the region in the first quadrant…

A: Disclaimer: ''Since you have posted a question with multiple subparts, we will solve the first three…

Q: (a) Assume that g(x, y) is a function of the form g(x, y) 0 if (x, y) = (0,0). (i) Show that g(x,…

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Q: Consider the function Step 2 of 3: Find lim f(x). x6+ f(x) = lim f(x) = x→-6+ x² + 12x + 22 19x +…

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Q: Question Find the average value of f(x) = - over the interval [0, 2]. Submit an exact answer using…

A: The objective is to find the average value of f(x).

Q: EXAMPLE 1(DISK METHOD) Find the volume of the solid generated by revolving about the x-axis,the…

A: Given problem:- EXAMPLE 1(DISK METHOD)   Find the volume of the solid generated by revolving about…

Q: problem: Find the vector below. ting the unit normal vector of A = 40 + 7 ₁ 0 - 3 K

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Q: Find the equation of the tangent plane to the surface f(x,y)=In(4x²-2xy-y²) at the point P(-1,-1,0).

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Q: In how many ways can 8 campers sit around a campfire? 5,040 5,760 40,320

A: No of ways n people can sit around a circle = (n-1) !

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Q: [u udv-uv- - [vdu to Explain why the substitutions below are inappropriate. Let dv =x dx 1. Suppose…

A: This questions uses ILATE  rule

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Q: x² + y² Briefly differentiate directional derivatives with suitable graph and equations.

A: This is a problem related to vector calculus. Based on the general formula and calculation we will…

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A: We know that if two vectors are perpendicular to each other then there dot product is zero. Given,…

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Q: (13+3^3)/4+4/2*6/12 020 011 030 ONone of the above

A: In this question, we will use order of operations.

Q: thi Prove that the improper integral } ] docdy (1 + x² + y²) ³¹²/₂ Converges

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Q: Question 12 of 12 >> Find all values of e such that the limit exists. lim x² + 6x + c x-1 (Give your…

A: The given limit is: limx→1x2+6x+cx-1 To find all values of c such that the limit exists.

Q: 2. a) Calculate the 4th roots of (5 - j3) b) Differentiate the following functions clearly showing…

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Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A: Given that     F(x,y,z) = x2i+y2j+z2k ,  We have to evaluate ∫∫sF.dS , where S is the boundary of…

Q: b) Calculate the following integrals x²(3x³ + 2)²dx (i) (ii) sin3x e³x dx (ii) (2x22+₁ +*²+2) dx S…

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