The binary operation defined as a+b=3a - 2b is closed in all the given sets EXCEPT set of Natural numbers set of rational numbers set of integers set of real numbers

Q: 3. Find the volume of the solid that lies under the paraboloid 5z = x² + y², above the xy-plane, and…

A: To find the volume of the solid that is bounded by given curves.

Q: Given that f(x): (a) (f+g)(-3) = (b) (fg)(-3) = (c) (fg)(-3)= (d) (4) | ( − 3) = x² 13x and g(x) = x…

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Q: Find the sum of the first 100 whole numbers?

A:

Q: Example 3: Find the parametric and symmetric of the line passing through the point (-3, 5, 4) and…

A: Here, the given equation of the line is: x=1+3t,y=-1-2t,z=3+t Therefore, the direction vector is:…

Q: Q1- Find all the second-order partial derivatives of the function: s(x, y) = tan-¹(x)

A: partial differentiation

Q: The displacement of a particle varies with time (t) as at^2-bt^3. the acceleration of the particle…

A:

Q: Evaluate 1¹ 1 - cos 2x sin 2x dx In | csc 2x + cot 2x | -ln | sin 2x | +C In 1|csc 2x-cot 2x |--In |…

A: The given integral is: I=∫1-cos2xsin2x   As we know the common integrals; 1). ∫cscxdx=lncscx-cotx+C…

Q: What value(s) of 8 are an appropriate choice when proving the following limit? lim (4x - 2) = 6 x-2…

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Q: A tank contains 420 liters of fluid in which 50 grams of salt is dissolved. Pure water is then…

A: We can solve the given problem by using the variable separable method.

Q: Find the Volume: Rotate the region bounded by y = 7 - x², x = -2 and x = 2 and the x-axis about the…

A: Volume of the solid of Revolution :  Suppose y=f(x) is a continuous non-negative function on the…

Q: Differentials: Determine the differential of the following: 3x² - 6xy+3y²-2x+2y-1=0

A: Given: 3x2-6xy+3y2-2x+2y-1=0

Q: If z is a variable, then the infinite series of the form is called n Σ" =a + a₁ + ª₂x² + ... + ª₂x”…

A:

Q: 6dx x - √ S 3√x²

A:

Q: Consider the following matrix. A = [22 -2] How many vectors are in the basis of row(A)?

A: Given: Now,                   30-3222Reduced matrix to reduced row echelon form:=10-1012The rank of…

Q: Show that lim in(+¹) + sin(+²) + n *** + sin(2) cos(1) - cos(2).

A: Above question is solved.

Q: Determine the area below y = 3 + 2x - x² and above the x-axis

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Q: wal u a Write the vector shown below as a combination of vectors and 7 shown above. a Vector - 21+ V…

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Q: 4 5 5 Let A = -1 -1 0 4 6 Use determinants to decide whether the matrix is invertible. Enter the…

A:

Q: What is the domain of the function f(x)= |x|? 0 (-∞,∞0) ○ (0,∞) 0 (-∞,0) ○ [0, ∞)

A: We need to find domain of given function.

Q: [s sin(√x)dx

A:

Q: Transfer this number (101010) from binary to octal 53 55 54 52 O

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Q: Use a Maclaurin series for sin x to obtain the Maclaurin series for f(x) = sin(x¹).

A:

Q: Solve for y esec(4y²-6y+14) = 3x + 1

A: To find the value of y , first, we take the logarithm on both sides of the given equation and then…

Q: Complete the parametric equations for the line where the planes - 7x + y + 3x = 3 and 4x7y + z = 23…

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Q: Use any method to determine whether the series converge. ∞ 1 (2) Σ 4k k=1 The series (5) Σ k=1 The…

A:

Q: Calculate lim h→0 9 + h-3 h

A: Find the limit

Q: 3. _1ffx,y) = tan—1 (), then X c) (x2 +y2)2 is ܐܐܐ )b ܐ)?x +y(

A:

Q: Cn = COS * ´π(1+4n)` 2

A:

Q: Using the Maclaurin series expansion of e, to find the series expansion of f(x). Express [ f(t) dt…

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Q: Use the translations to graph the given function. Show all of the transformation on the same graph.…

A: We have to find transformation

Q: Solve the following x³-x²-√√2x limx→2²-11x+18

A: Above question is solved.

Q: ff is continuous and ƒ(5) = 2 and ƒ(4) = 3 then lim ƒ(4x² — 11) = 2. x→2 True False

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Q: (2x -۱۱۶ (3x44795

A:

Q: Q3- Sketch the region of integration and evaluate the integral: In8 lny [TD [t ex+y dxdy

A: Given problem:-

Q: Consider the function f(x) 1 1-x²

A:

Q: Sketch the graph of a single function f(x) that satisfies all of the following conditions, labeling…

A: The function satisfies the condition,The domain of fx is -∞,∞f'x=5x2x2-3f''x=10x2x2-3f0=0

Q: 6dx S: ³√x² x-

A:

Q: 4. A 25-ft long ladder is leaning against a vertical wall. The foot of the ladder is on a horizontal…

A: To solve the following problem.

Q: Solve for x sin (log2 (13x² + 16x34) = y

A:

Q: Please write the complete solutions. Upvote will be given! Consider the region bounded by y = x3, y…

A: Please write the complete solutions. Upvote will be given!   Consider the region bounded by y = x3,…

Q: Evaluate 1₁ 2 t(1 + Int)² dt

A:

Q: Solve the following LONG DIVISION 6x³5x249x equation by using + 60 = 0

A: To solve the equation by long division.

Q: Solve for y esec(4y²-6y+14) = 3x + 1

A:

Q: Calculate lim X→-2 x³ + 2x² - 1 5 - 3x

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Q: Find the length of the curve y= 2²-√√x, 4 ≤ x ≤9. 23/2 3

A: To find the length of the given curve.

Q: Show that the differential equation x²y³ + x(1+y²)y' = 0 is not exact, but becomes exact when…

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Q: Find dy dx G. y= = 20 In (e 5* +20) b. y = 20x (220x) c. y = €²0x-1 + 20 (n (ex)

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Q: Determine the area of the region bounded by the curves y = ₁, y = 2x and x = 4

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: 17/45 100% + Example 3: Find the parametric and symmetric equations of the line passing through the…

A:

Q: Given the function f(x) = {2ª 2x x 2 which statement is FALSE at x=2? O The derivative from the…

A: