Question 5 fx²√3x dx is equal to 0 -27 (3 - a) 3 - -5 7 (3— æ) +15√(3-x) - + 2 2 -5 0 æ) −3 (3 – a) 12 (3 – æ)^ _2 (3 – 1) - 0 + + 2 5 -5 0 293-14 c 3√(3 - x)³ - 12 (3 – 1) 2 (3 – a) I + 2 5 0 27 (3 – æ) 7/(3 − 1) +-5₁√(3-x)³ + 20 2 2

Q: Question 18 Find - y dy (y + 2 A(√y+2-5) (5√/y+2+y+24)+C А Ⓡ(√y+2-5)(-5√/y+2+y+21)+C B Ⓒ(√3+2-5)…

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Q: Determine why dx converges or diverges.

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

Q: 19. dx 1 Je²x_8 2x -8

A: The solution is given in the next steps.

Q: Write as a single function of a single angle. tan 145° tan 85° - = [?]([_]°) 1+tan 145°. tan 85°…

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Q: 53 3-2x-x²

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Q: 2. Given u = 8i - j + 3k and v = 7j - 4k, compute each of the following. (a) -3v (b) 12u + v (c) ||…

A: In this question, we have given two vectors u and v. We want to compute the given expression.

Q: dx 3-2x-x²

A: We need to solve : ∫-10dx3-2x-x2

Q: A ream of 500 pieces of 8½ inch by Il inch copy paper has a volume of 280/2 inches³. What is the…

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Q: QUESTION 2 Evaluate lim " QUESTION 3 Clearly illustrate with explanations why lim 100 0.01F g(x) x-0…

A: We have to find limit

Q: What is the solution to the differential equation 2√√ay- da Oy = ( ² √₂-2) ? 3 Oy=(2²√x - 2) ³ 1 =…

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Q: Differentiate: y(x) along the curve xy =ex Show all working out.

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Q: y = 4 16 3x+3

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Q: A spherical tank of diameter 4 m is half-full of water (weight density - 9800 N/m³). Setup the…

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Q: Find y dy ·S- using the substitution +5= √√y+2 U /y+2 /y+2−5) (5√√y+2+y+24) + C…

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Q: π Find the area bounded by the trigonometric curves y = sinx and y=cosx" from X=- 3.459 square units…

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Q: Covered topics are Applications of Definite Integral: Plane Areas and Areas Between Curves and…

A: We have to find volume generated by given condition.

Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…

A: Being carefule to allow for parts of the curve being both above and below the x‐axis, to determine…

Q: 14. sec xdx 2 3/2 (1 – 4 tan x)³/²

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Q: Evaluate tan" (x) sec¹x dx. 1 1 (A) -tan (m+2)(x) +· ¹tan" (x) + C - m+2 m 1 1 (в -tan (m+3)(x) +…

A: On solving this we will get Option (B) is correct

Q: True/False 1) d[f(x) g(x)]/dx= f'(x)/g'(x) 2) d[f(x)]"/dx= n[f(x)] f'(x) and…

A: This question is based on diffrentiation and integration.

Q: S (2 + x)dx √4-2x-x²

A: We can solve the integration as below.

Q: Where does the line through (-3, 1, 0) and (−1, 3, 8) intersect the plane 2x + y − z = -2? (x, y, z)…

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Q: 14. Solve the initial-value problem dy dt = -2y + u₂(t)e¯¹, y(0) = 3.

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Q: QUESTION 1 In x Complete the following table to evaluate the limit lim X-00 √x Step Explain the step…

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Q: A spherical tank of diameter 4 m is half-full of water (weight density = 9800 N/m³). Setup the…

A: Given the spherical tank with diameter 4m So the radius of the spherical tank R = 2m Weight density…

Q: ·S- Find y dy Vy+2 using the substitutionu +5=√√y+2. A √y + 2 − 5 ) ( 5 √√y + 2 + y +24) + C (В…

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Q: 20. [(x²+2x-10/3 (5x+5)dx

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Q: 3x³ -dx. Using the method of partial fractions, the given integral can be written as 3x4+6x3 3x2 -…

A: Here, 3x53x4+6x3-3x2-6x=3x53x(x3+2x2-x-2)=x4(x-1)(x+1)(x+2)=x-2+5x2-4(x-1)(x+1)(x+2)

Q: What is dy/dx of the given function ³ - 2y² = 6 ? 0-²2 3:² CHE o 3,212

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Q: Evaluation. 1. f5x³-³ dx √x3 Determine the antiderivative for each. Show complete solution. 2.…

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Q: Find the area bounded by the curve y=- 16 (A) 16 square units B) 10 square units 8 square units D 4…

A: If y=f(x) and y=g(x) are two continuous function on a,b and f(x)≥g(x) on a,b , then area bounded by…

Q: Find the area bounded by the curve y = 16 A 16 square units (B) 8 square units 10 square units 4…

A: Find the area bounded by the curve y= 1/16x3-3/4x2+3x and the line y= x .

Q: QUESTION 3 To evaluate x²cosx dx' x’sinx+2x cost – 2 x’sinx − 2x cosx+2 x’sinx – 2x cosx – 2 x’sinx…

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Q: What is the f(7) (-2) of f(x) = - +2x - 7x³ + ³² + 5x +1? 3x² 2

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Q: Which of the following is or is not an improper integral? Clearly explain your choice. A. ₂dx B. dx…

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Q: Question Use the left-endpoint approximation to approximate the area under the curve of f(x) = +2 on…

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Q: If a particle moves on a straight line so that s = et (cost – sint) . Which expression can be used…

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Q: Stoe 0 ex dx Evaluate: A 0 (B) e (C) + ∞ (divergent) D 1 E) None

A: ∫0+∞e-xdx here ∫e-xdx =  -e-x

Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…

A: This question is related to definite integration, we will solve it using given information.

Q: fx²cc use integration by parts. What is the expression after the second integration by parts? x2sinx…

A: Solved below.

Q: Evaluate A B D Stan" tan" (x) sec4x dx. —tan (™+3)(x) + _____tan (™ + 1)(x) + C m+1 1 −tan (™+2)(x)…

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Q: the correct steps to evaluate cos²20 dº is 0 One of Ⓒ[-[²04 A de sin²20d0 0 0 [1²4] B de- cos 40d0…

A: We use double angle formula  cos(2x) =2cos2(x)-1  cos2(x) =(1+cos(2x))/2

Q: If $S² A 2x²+x-2 (x+1)(x²+1) (В NIG NI- S None -dx= B(2x) +C1 14.0+. dx, then the value of B is…

A: We can answer the question for the value B as below.

Q: The volume of the solid generated by revolving the region bounded by x2-4y and y2 = 4x about b using…

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Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…

A: Area is shown below÷

Q: (D³ - 2D + 4)y=0; y = -2, Dy = 8, D²y = 0, when x = 0.

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Q: Find integral fraction (numerator) y dy / (denominator) square root of (y+2) using the substitution…

A: Let's find given integration by using given substitution.

Q: Use the table to the right to find the given derivative. d xxx) 1x=5 (Simplify your answer.) |x=5 X…

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Q: y dy Find ·S- using the substitution +5=√√y+2· Vy+2 ²(√y+2−5)(5√/y+2+y+21)+C 3…

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Q: If " (x+5) dx = 14, then the value of b is equal to A) None B 2 (C) 4 D -3 (E) 3

A: Given