Let f: CD be a function, with C being the domain and D being the codomain. Show that for any C₁, C2 C C f(C₁ C₂) = f(C₁) ₪ ƒ(C₂)

Q: 3 So² √(√₁² - ²√₁²³) ²³ a dt

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A: Given x→=2i→-3k→ & y→=i→+5j→-4k→To write expression in terms of i→,j→,k→:

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A: We will use chain rule to solve this question.

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Q: 21. Find lim x-5 A. 2 B. 3 x² - 7x+10 x-5 C. 4 D. 5

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

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A: Area=L×W=2500 m2 So,L=2500W The perimeter P=2L+2W+2W {to divide the field into three 2 fences of W…

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A: Since the student has posted multiple questions and does not mention any specific question, so we…

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

Q: Given x = y³+2y — In(y + 1), find the arc length for 0 ≤ y ≤ 3 B

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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.

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Q: iven R'(t) = (4e²t, 2t ,2cosh t), and R(0) = (1, −2, 3), 1+t² find Ŕ(t), and give the parametric…

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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

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Q: 27 3. Explain how you would find the general term of the sequence: 4, -6, 9, - ".

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Q: Find the volume generated by revolving about the y-axis the area bounded by y2= x-2, y=x-4 Use shell…

A: Here we have to find the volume by using shell method.

Q: What is the inverse for the function f(x) = 2+3/1-x? A. f1(x)=1-(x-2)³ 1 B. f¯¹(x) = 2+³/1-x C.…

A: Given that:  f(x)= 2+ (1-x)1/3 and we find the value of f-1(x).   Here i attached the solution of…

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

A: Solved below.

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Q: (-1)k 9. Does the series Ex=1 +7 converge absolutely, converge conditionally or diverge? A.…

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

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Q: For the following problems, find the general solution. 128. y" cos(x) + 2y + y

A: To find the general solution of the following differential equation.y''=cosx+2y'+y

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Q: TYPEWRITTEN

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Q: Evaluate the y' and Simplify the answers I Direct trigo functions y = x² sinx + 2xcosx - 2sinx

A: The function is given by y = x2sinx+xcosx-2sinx To evaluate: The first derivative of the function.

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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: d/dx(arctanh(2x)) 2XIn2 A. 1-4X 2x B.- 1-4X 2 In2 C. 1+2x 2x D.- 1-2x

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Q: 1. Evaluate the integrals (a) fxsin 2xdx, (b) f(3x - 1) eª dx, Hint: Use the Integration by Parts. 3…

A: SOLUTION-

Q: T/6 3 coss 3x dx

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Q: A company determines that its total cost, in thousands of rands, for producing x  items is (image…

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Q: Using the method mentioned in Item #7, find the volume of the solid generated by 3 revolving the R…

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

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Q: x-4 x²+2x-15 Inx+51-Inx-31+ C 8 Option 1 S: dx 1 (x + 5)⁹1 Je In + C + x-3 -100 1 9 In|x + 5|ln|x −…

A: We can find the answer as below

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: The trough in the figure is to be made to the dimensions shown. Only the angle can be varied. What…

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Q: Consider the vector-valued function R(t) = (t³-t, 2t², 2 - 21²). 1. Find ||'(t)||. (Simplify your…

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Q: The most convenient way to evaluate A) True B False 2x-3 S- -dx is use Integration by Parts. x²-3x+5

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Q: Jane is 2 mi offshore in a boat and wishes to reach a coastal village 6 mi down a straight shoreline…

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Q: Evaluate the y' and Simplify the answers I Direct trigo functions y = x² sinx + 2xcosx - 2sinx

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Q: 26 Find the value of k so that line 4, 2]-[2-20]++ [2, k₁-3) is parallel to the Plane *x+24-42=12

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Q: Find the average value of the f(x) from z = 10 to z = 16 f(x)= √² - 100 I

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Q: The curve y area. = √x + 2 is revolved about the y-axis from x = 1 to x = 8, find the surface

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Q: What integration technique can be used to integrate: O Integration Formulas O Trigonometric…

A: Use integration by parts and substitution method.

Q: Find the area bounded by the parabolas (x - 2)² - 9py = 0 and y² = 9p(x - 2).

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Q: Consider the plane : x + 3y - 2z = 6 and the line with parametric equations l: x=4-3t, y = 2+t, z =…

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Q: Find the slope of the tangent line to the graphof the polar equation 1 r = at Ø= 1-sinø 6

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Q: Solve the following trigonometric equation for 0 ≤ 0 < 2π. Show your work. 4 cos²x 3 =

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