POT Q3.If f(x,y) = sin'(x-3y) +sin xind: of af and ду

Q: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…

A: Given:         Density of Liquid ρ=9000 N/m3          Sides of triangle a=2 m     The expression for…

Q: Two sides of an oblique triangle are measured as 80 ft and 100 ft and the included angle as 60°. If…

A: I am attaching image so that you understand each and every step.

Q: QUESTION 16 y dy Find of- using the substitution +5= √√y+2 √y+2 ² (√√y+2-5) (-5√/y+2+y+21) + C…

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

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Q: y = 4 16 3x+3

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Q: 5. Evaluate , x dV where S is the region (solid) bounded by x = 0 and x =

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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: y" + 4y= cos²x

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Q: Evaluate tan" (x) sec4x dx. 1 ¹__tan (m + 1)(x) + ___¹__tan (™− 1)(x) + C A. m+1 m-1 1 1 -tan (m…

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Q: 1 Find the area bounded by the curve y=- =-=-—-—-x³-3³² x ² + 16 4 -x2 + 3x and the line y=x.

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Q: 10. 3 J√cos z sin ³ zdz COS

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Q: Find y dy S using the substitution u +5=√√y+2. √y+2 A (√9+2-5) (5√3+2-1+24) +0 B (√y+2-5)…

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Q: find the values of λ for which the determinant is zero. 2 λ + 1 0 0 1 O(-1, 1, 1) O(-1, 1, 0) O(-1,…

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

A: 16)Given,y=x316-3x24+3x and y=x

Q: What is the solution to the following initial value problem? dy + 4x = 3 y(0) = 1 da Oy=-2x² + 3x -…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)2=2y, the…

A: Please see the below picture for detailed solution.

Q: Exercises To Solve [No.5] 3dx 9x²-6X+5 1

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Q: 6) INVERSELY LOGARITHMIC The following information is given about a logarithmic function of the form…

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Q: Evaluate tan" (x) sec¹x dx² A −tan (m+2)(x) + — tan” (x) + C m+2 1 −tan (m+3)(x) +_¹__tan (m+1)(x) +…

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Q: If 10 fro A True B) False f(x) dx = 17 and 8 Lof(x) d f(x) dx = 12, then 10 ["fo f(x) dx=5

A: ∫010 f(x)dx = 17 ∫08 f(x)dx = 12 ∫810 f(x)dx = 5

Q: S tan³ √√√x X X dx

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Q: 3cos(6x) How can this value be converted to sin How much is it in sin?

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Q: Evaluate A B e Stam" (x) sec³x dx- -tan (m+3)(x) + m+3 1 m+2 -tan (m + 2)(x) + m −tan (m + 1)(x) — —…

A: Solved below.

Q: 2. 2 4 Scot² 3x csc + 3xdx

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Q: 11. fel/x²di .3 X хр

A: Here, to evaluate: I=∫e1x2x3dx

Q: For x 1/2 -dx and using the substitution u=x 1/2, the resulting integral takes the form: x-x 4u -du…

A: We can rewrite the given integral by using this substitution u = x1/2

Q: y dy Find S² using the substitution u +5=√y+2. √y+2 (A) (√3+2-5) (5√3+2+y+21) +C 3…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)2=2y, the…

A: Please see the below picture for detailed solution.

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

A: We need to find area.

Q: 25

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Q: QUESTION 18 Determine the third order MacLaurin's polynomial for f(x) = ex.

A: Kindly note that I have authority to answer only one question. If you want remaining question to be…

Q: 18. S sin xdx 2-cos² X

A: The given integral is: I=∫sinx2-cos2xdx    ...1 As we know the common integral; ∫11-x2dx=sin-1x+C

Q: Question 1 1 Define Q as the region bounded by the function f(x) = x and the line x in the first…

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Q: y dy y+2 (√√y+2=5)(-5√√y+2+y+21) + C 3 B (√√y+2-5) (5√√y+2=y+24) + C 3 © ²² (√√y+2-5) (5√/y+2+y+24)…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by , the x-axis, and…

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Q: Given that f is a differentiable function with f(3, 4) = 8, fx(3, 4) = 1, and f,(3, 4) = −1, use a…

A: We have to find the value of function by linear approximation.

Q: Evaluate sin (Inx) dx. Integration by parts will be used repeatedly. What is the expression after…

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Q: √x(y)²-(√x cos √x - sec √x)y'=1

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

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Q: If S A 2x²+x+1 (x-1)(x+1)(x-2) 11 3 -2 11 3 None 1 E - 3 C dx = А SA + B C + 1 + = -₂2]dx x+1 + dx,…

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Q: c) Parametric equations of a line that goes through P(1, 3, 5) and is perpendicular to the line (1,…

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Q: +√√² cas² S 4 cos²20 de is One of the correct steps to evaluate @ 1²00-1/²160²20 4 de- A sin²20d0 Ⓒ…

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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: What is the definite integral represented by the limit lim (+4) Ax, on the interval [-1,1]? n-x •…

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Q: A trough is full of liquid of weight density 9,000 N/m³. The ends of the trough are equilateral…

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Q: y dy Find 13 using the substitution +5=√y+2. √y+2 A ²/ (√x+2-5) (5√/y+2-y+24) + C 3 B (√9+2-5)…

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Q: y dy Find S √y+2 A(√3+2-5) (5√3+2+y+24) + C B (√y+2-5) (5√/y+2¬y+24) + C 3 Ⓒ²(√x+2-5)(-3√x+2+y+21) +…

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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: Question 15 Find the area bounded by the curve y = -x 16 A 8 square units B 16 square units C10…

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Q: The integral O x dx can be transformed to which of the following using trigonometric substitution?…

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