Prove Formulas (1) - (9) Differentiate y = √3x². - 1 √5x = = (3x²)¹/³ – (5x)−¹/2

Q: S N

A: Use ratio test for checking the radius of convergence

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A: We have to find the general solution of the given differential equation using variation of…

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

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Q: 1. Vector A is the same as: (Circle ALL that apply) A a. B+C b. D-B B C. D+C D d. (D-C)

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Q: Text Canada's population is about 33 million people. It is increasing at about 1.8% per year. How…

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

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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: q4

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Q: 4. Verify the final value theorem for the function 3t²e-4t and determine its steady state value.

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Q: The population of a town is decreasing at a rate proportional to its size. In 1980, the population…

A: The population of a town is decreasing at a rate proportional to its size.In 1980, the population…

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: Find the equations of tangent and normal lines of the curves at given points: y²-3xy - x = 0 at(2,8)

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Q: Find the Area of the Surface obtained by rotating the curve about the y y = √√x, 1 ≤ y ≤2

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Q: Find the Area of the Surface obtained by rotating the curve about the x - axis y = cosh x, 0 ≤ x ≤ 1

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Q: If f(x) = 10, find f'(-1).

A: Given f(x)=10,  to find f'(-1) Formula used Differentiation of a constant value is zero d (constant)…

Q: Find the area bounded by the parabolas (x - 1)² = 4ay and y² + 4a = 4ax.

A: Here we have to find out the area between the given curve that is we have given two parabolas

Q: In an autocatalytic chemical reaction, the product form is a catalyst for the reaction. If Qo is the…

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Q: Find the derivative of f (y) = 153/g In(y)

A: Given: f(y)=15y3lny

Q: I co cos³ x sin x dx

A: Given problem:- ∫cos3(x) sin(x) dx

Q: 2x fe²x sinx dx

A: Using integration by part.

Q: Evaluate the following integrals. -1 L₁ (3²- (3x² - 4x−¹+2) dx

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Q: ly If cosh x = then sinh x = Select one: True False If f is continuous on a closed interval, then f…

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Q: 1- Find the inverse of 2=2-51.

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Q: _42. Evaluate: √(√√x - 2)dx 3 A. ++ C x 3 B. - + C x C. 3 +=+ C 2 D. -*²_³+C 2 x 12 Evaluato: ((2x…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 2) Let f be continuous on [a, b], differentiable on (a, b) and positive (i.e., > 0) for all f'(c)…

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Q: Consider vector v = (1,2,2), point A(2,5,4) and point B(-1,5,1) - In center-radius form, find an…

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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: Evaluation. Determine the antiderivative for each. Show complete solution 1. S dx 5x³-3 √x3 2.…

A: As we know that; The Sum Rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1       1).…

Q: x3-4x-10 x²-x-6 dx.

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Q: 4. Determine the Cartesian equation of the line that... a) is perpendicular to x=2+t, y=-3 + 2t and…

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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: 2- Compute 1+i 2-51

A: Given that,      1+i2-5i

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: rve (y+1)2 = 4x3 from x=0 to x=1? (4) =q8

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Q: Use f(x+0.0001)-f(C) 0.0001 f(x)=52²-7x ata = 2, to the nearest tenth. to determine the…

A: Given function f(x)=5x2-7x

Q: f(x)=8x¹-7x³+2 on [−2,1]

A: To compute the average value of the given function f(x)=8x4-7x3+2 on [-2, 1]

Q: The area bounded by the parabola ay=x², the x-axis, and the line x=b is revolved about the y-axis.…

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Q: 6. Determine the Cartesian (scalar) equation of the plane that... a) contains the points (6,1,0) and…

A: SOLUTION-

Q: _ ²+2y — In(y + 1), find the arc length for 0 ≤ y ≤ 3 8 Given x =

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Q: Determine the equation of one of the curves for dy/dx = 4x which passes through the point (2, 3).…

A: We need to find a curve for dydx=4x which passes through 2,3.

Q: example of properties of definite integral

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Q: Given: planes ¹: 2x - 5y+z=-1 and 2: x + 5y+z=5 intersecting on a line . (a) Determine the symmetric…

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Q: 2.which of the ff.is the reverse process of chain rule?a additional rule b.product rule…

A: Reverse Process of Chain Rule:       The chain rule for derivatives allows to calculate the…

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: Calculus Please Show

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Q: Determine the center-radius Form of the equation of the sphere who diameter has endpoints at (2, -3,…

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

Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

A: I have shaded the area green which is to be calculated

Q: Given the function f(x) = = Find the difference quotient Find f'(x) by determining lim f(x +h)-f(x)…

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