-2 Evaluate the integral: ² ft² n s teu du ds dt

Q: 3 Evaluate: (4x²yz - z dz dy dx 24

A: The integration of the triple integral is (4x2yz-z4/4), z from 0 to 1, y from -1 to 4, x from 2 to…

Q: The derivative of y = sin(e2x) is: 1. e2xcos(e2x) 2. 2cos(e2x) 3. 2e2xcos(e2x) 4. 2xcos(e2x)

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Q: f(x, y) = ln(x² – 25) + √√-y² - x² – 10x . -

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Q: -3 Evaluate: ²¹²² ²³ y cos(z³) dx dy dz

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Q: Define R as the region bounded by the functions f(x): = 3 and g(x) = x + 1 between x = 0 and x = 1.…

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Q: A) Match each equality with the letter corresponding to the property it illustrates. Responses may…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Evaluate: ƒ²₁ ³² ²₁ 0 [(x²-y²)²] x+y du de

A: Follow the procedure given below.

Q: ¡xr-¹e-λx, x>0, r,λ > 0. Given f(x) Γ(r) 1. Find f(x)dx.

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Q: True or False: Given a vector v, the vector -v will have an opposite magnitude. A True B False

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Q: 5x 3 2 Evaluate: ffxf²dz dy dx 2

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Evaluate: xy² dx dy

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Q: Evaluate: ²₁²²-²² du (x²-y²)²] S du dt x+y

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Q: Let f(x) = e2 sin x 1. Use the local linear approximation of f at x = 0 to approximate e2 sin (0.01)…

A: 1.          given is f(x)=e(2sin(x))f(0)=e0       =1f'(x)=2cos(x)e(2sin(x))f'(0)=2linear…

Q: A small high school has 35 seniors, 25 juniors, and 15 sophomores. If 3 students are chosen from…

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Q: 1. Perform the following integration. 1. | (sinh a)(coth® a + cscl® a) da

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Q: π/3 So, f²ef/³ t In u tans ds du dt

A: Given problem:-

Q: 2. Evaluate all of the integrals. r² sin r dr

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Q: ع لح ل(۸ + ")APNPLPLg للع(۸

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Q: f(x)=2x+1(3x-1)

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Q: Evaluate: ³₂(4x²y — z³) dz dy dx

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Q: Does the Rolle's Theorem applies for f(z) – ln(2 – z²) over the interval [−1, 1]? O Cannot be…

A: This is a problem related to derivative of the function. Based on the general formula and concept we…

Q: Q2. Use Lagrange Multiplier to find the point on the circle: x² + y² = 45 that are closest farthest…

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Q: (x + 2)" Q4. Find the convergence interval and radius of the series : Σ (-1)**² n=l n

A: We need to find interval and radius of convergence.

Q: 3. Determine if the assigned improper integral is convergent or divergent. Lever e²+1 dr

A: Given problem:-

Q: Using the Mean Value Theorem, given f(x) = x³, what is/are the value of c, where 0 < c < 2 such that…

A: Topic = Functions

Q: ¹₁1+x²x+2y dy dx

A: We need to evaluate the following iterated integral as following: ∫-11∫2x21+x2x+2ydy dx

Q: Evaluate the integral: 2² sin (²) dt du

A: To evaluate the integral: ∫π2π∫0u2sintudt du

Q: Find the area of the region bounded by the curves 1 y = (x+4)²¹ Y = 4 and the x-axis using vertical…

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Q: dentify the surfaces of the following equations by converting them into equations in the Cartesian…

A: The given data is: To identify the surfaces: z2=4+4r2

Q: Find the coordinates of point C using the data given below. • Write your answer in this format : Y-X…

A: Concept: For the triangle ABC coordinates are       Y(m)             X(m)A    2784.57     3500.64B…

Q: x² Define R as the region that is bounded by the graph of the function f(x) = 2 +2, the x-axis, x =…

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Q: B. Find the area bounded by the curves, the axis and the given values of y. Sketch the graph. 3.…

A: Given problem:- B. Find the area bounded by the curves, the axis and the given values of y. Sketch…

Q: What is the lim 700 (n-1)-1 + (n − 2) x^²-2 +...+ OB. undefined O.D. 22-1 ne2+7

A: Here, to evaluate: limx→∞xn+xn-1+xn-2+...+x(n-1)xn-1+(n-2)xn-2+...+x

Q: Evaluate the double integral: y LL (Hint: Change the order of integration to dy dx.) dx dy.

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Q: Determine the derivative of the following function. Do not simplify. y = ecosxsinx

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: Given that  The Region bounded by the curves  y = 4 + sec(x) , y = 6 ,  -π3≤x≤π3  about y = 4…

Q: Evaluate: ³²₁₂[z³(x + y)³] dz dy dx

A: Given, ∫-43∫-12∫01z3x+y3dzdydx

Q: Find the equation of the logistic function with a maximum value of 1000, an initial value of 500,…

A: Topic:- function

Q: What will be the orientation of the curve of the graph of the function f(x) = 3 on (-3,0)? z² z+3 O…

A: Given the function  f(x) = x2x+3 on -3, 0.

Q: solving the following differential equations (x + tany)dy=sin ey dx

A: On solving this we will get

Q: Evaluate: 1+ 2y dy dx •x x2

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Q: -2 Evaluate: ²₁²[(x²-²²] 0 x+y du dt

A: Topic = Integration

Q: Evaluate the integral: .0 ²/3 t ln u tan s ds du dt 2e π/3

A: Given: ∫-10∫e2e∫0π3t lnu tansdsdudt

Q: Evaluate the integral: f/2² sin (-) dt du ,2

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Q: What is the direction of the vector with an initial point of (3,-5) and a terminal point of (8, 6)?…

A: The initial point is (3, -5) and the terminal point is (8, 6)

Q: Find the value of the following definite integrals. Show your solution. L₂(x¹+4) dx 2. (cos x + tan…

A: Topic = Integration

Q: Evaluate: √₂²³ Sª₁ S₁ (4x² yz — ) dz dy dx -

A: This is a problem related to triple integral. based on the general formula and concept we will…

Q: Evaluate: xy² dx dy

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Q: Find the area of the region bounded by the curves y = 1 (x+6)²¹ į, y = = 4 and the x-axis using…

A: Explanation of the answer is as follows

Q: Question 8 Determinethe equation of the tangent line to the curve, y = 3x4-2x-1 4-x² , at x=1.

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