ng exercise, evaluate the integrals of the functions graphed using the formulas for a circles, and subtracting the areas below the x-axis. √-72 +18x - x² √2x - x² 2 8 10 0 4 6 |x - 41-2 12X

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Q: 6. If f is continuous and f² f(x) dx = 6, evaluate S/² f (2 sin 0) cos de.

A: see below the answer and calculation

Q: -x+1 3+z Given the points R (1, -1, -3), the vector v = and the line d: = 1 + y = 3 2 1. Determine…

A: Both questions are solved.

Q: 2. z = x + 2 У Х x

A: Solution

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A: We have to find the area of the region bounded by y2=4ax and x2=4ay.

Q: Find the derivative of f (y) = 8 tan (y) V √y 8 8 √Y y4

A: The given function is: fy=8tany-y8-8y4y As we know that; The Sum/Difference rule: f±g'=f'±g' The…

Q: 22. Suppose that lim f(x) = x, what is the value of lim 5. (f(x))² ? x-3 A. 41 C. 45 B. 43 D. 47 23.…

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Q: 5. Find the derivatives (a-b) and the limit (c): (2) ± √( 1 cos (1²) dt) (0) ² (154) dt dx 1 r2+x…

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Q: _11. If lim (x² +1) = 2, and x = 2.5, then x->-1 lim (x² + 1) is equal to. x-2.5 A. 5.25 C. 6.25 B.…

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Q: i can't understand your solution

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Q: Question 2 Determine the general solution. x (dy/dx) = 2 - 4x^3. O y=lnx-(1/3) x^2 + c Oy=2…

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Q: f(x)-f(a) a. Use the definition mtan = lim x-a x-a b. Determine an equation of the tangent line at…

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Q: e formula C = (F-32), where F2-459.67, expresses the Celsius temperature C as a function of the…

A: Topic:- function

Q: Ex: If w cos(uv), u = xyz, y = TT 4(x²+y²)' aw find at point (1, 1, 1). əx

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Q: 2x³ - 4x² − x − 3 dx x² - 2x - 3 zln |x+1| +31n|x - 3| + C Option 1 2 In x + 1-3 ln|x - 3| + C…

A: Given, ∫2x3-4x2-x-3x2-2x-3dx

Q: 3 S ₁² √ (²√₁² - ²√+²) ³ dt

A: Given

Q: d dx A.sinh(Inx) B.–sinh(Inx) sinh(Inx) C.- X -cosh(x) D. X cosh (Inx) =

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Q: 23. Test the series below for convergence using the Ratio Test. Σ n2²n 8n-1 n=1 The limit of the…

A: Here we have, ∑n=1∞n22n8n-1

Q: Solve the differential equation a. (4x³y² - 6x³y - 2x - 3)dx + (2x¹y-2x³)dy=0 b. (x-4y-3)…

A: If the differential equation Mdx +Ndy =0 is exact i.e, ∂M∂y=∂N∂x ,then solution is        ∫y…

Q: Find a set of parametric equations for the curve of intersection of the paraboloid z² +4y² -z = 0…

A: Here, to find the parametric equation of the paraboloid x2+4y2-z=0 and the plane 2x-z=0

Q: Find the moment with respect to the y-axis of the area bounded by the parabola x = 9y - y² and y =…

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Q: 3. Find a vector equation of the line that... a) passes through (-3,5,-2) and (7,-3,1) b) has…

A: vector equation of line

Q: Given x - ³²+2y — In(y + 1), find the arc length for 0 ≤ y ≤4 8

A: The arc length of the curve x=f(y) for a≤y≤b is given by ∫ab1+dxdy2 dy

Q: cos 3x cos 4x dx

A: ∫cos3xcos4xdx here we use formula  2cosxcosy = cos(x+y) +cos(x-y) here x = 4x      y = 3x

Q: INALTIIX Large Drop-Fro... Summary - Qui... George Floyd: '... Paraphrasing T... when did geor...…

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Q: In the quadratic equation Ax²+BX+C =0 The roots are real and distinct. The roots are complex…

A: The given quadratic equation is Ax2+Bx+C=0

Q: Consider the point P (-3,-1,5), the line : x = 3 t. y, y = -6t -3₁ z = 2t +1, and the Flane 1² : 7…

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Q: Given: planes II₁ : 2x - 5y + z = −1 and II₂ : x + 5y + z = 5 intersecting on a line l (a) Compute…

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Q: -0.45|-2.8x - 4.06| 2.5

A: Here we have -0.45-2.8x-4.06-2.5

Q: 6. If y = 3√x, then what is y'? A. y' = C. y' = ¹ x 3 x3 B. y' = 1/2 D. y' = ¹/2/2 x3 x 3 7. Which…

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Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y=-2 about the…

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Q: Show that the three functions: f₁(x) = ex-8f₂(x) = exf3(x) = 4(2x-2) are linearly dependent.

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Q: z²√(-z² + 1)5 dz

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Q: Determine the x- and y-intercepts for the given function. B(x)=5x+8

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Q: B. m(x) = D. h(x) = x+2 x²-4 28. What is the removable discontinuity of x²-4 the function f(x) : = ?…

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Q: 2 5 6z³ -8z¹+2z² 4 Z dz

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Q: 1. Solve the differential equation (x-4y-3) dx-(x-6y-5) dy=0

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Q: Question 4 Solve y at x = pi/3. cotx dy/dx = 1 - 2y, y(pi/4) = 1 0.75

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Q: Find the area bounded by the curves -x + y² = 8, x = -2y and y = -2.

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Q: given below. t lim f(x) = -8, lim g(x) = 5, and lim h(x) = 4 X-C X-C X-C 17. Find lim[f(x) = g(x)]…

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Q: The volume of a cube is increasing at the rate of 4cm³/min. How fast is the surface area increasing…

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Q: Find the volume of the solid generated by the region bounded by y - x² = -3, x+y = 3 about y = -5.

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bound by…

A: Volume of solid is evaluated using cylinderical shell method.

Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

A: This question can be solved using the concepts of application of derivatives.

Q: · ƒ³3(x + 1)(x + 2)²(x² −1)dx with and without the even-odd theorems (show both solutions).

A:

Q: a. Use the definition mtan = lim f(a+h)-f(a) h h→0 b. Determine an equation of the tangent line at…

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the…

Q: 2. Verify using the principle of Superposition that y₁ = ²* and y₂ = e* are solutions of y" - 7y'…

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Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the…

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Q: Find the area bounded by the curves y-x² = -3,x+y = 3 and y = 0.5x.

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