Suppose that 3 of work is needed to stretch a spring from its natural length of 30 cm to a length of 45 cm work is needed to stretch the spring from 35 cm to 40 cm- O 2.08 J O 1.04J 01J 021 How much

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A: The graph of the function is To evaluate: The value of limx→4fx

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Q: 1-x x² +1 If f is differentiable function with deriviative f'(x) = - then on which of the following…

A: f is concave up if f''(x) >0 .

Q: A) A retailer has been selling 1,000 computers a week at $750 each. The marketing department…

A: Please see the below picture for detailed solution.

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A: Given problem:- A rectangle fence was installed yesterday around gemma's house. The students from…

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Q: dy dx 4x + y 2x+y

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A: see below the answer and calculation

Q: 4. General solution of dy= y-x dx y+x

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Q: A circular swimming pool full of water has a diameter of 24 ft and the sides are 5 ft high. Set-up…

A: A circular swimming pool full of water has a diameter of 24 ft and the sides are 5ft high.

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Q: Solve the Ordinary Differential Equation by Laplace Transformation y" - 2y' - 8y = 0 if y(0) = 3 and…

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Q: 7- Deteremin all Max and min value of y= xe* +3e³

A: Given that  function   y = xex + 3e3         ........……........(1) Now  differentiate eq. (1) w.r.t.…

Q: f(x) = In X X

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Q: 7* +(7)* 2 7. If А. 2 О A О в О с о D оо =1 then x= B. 4 С. 1 D. 0

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Q: f(x) = x³, Y Find the volume of the solid obtained by rotating the region A about the x-axis. A B

A: The region A is bounded by y=1 and y=x3 from x=0 to x=1

Q: 3 For y = f(x) = 6x³, x=4, and Ax=0.05 find a) Ay for the given x and Ax values, b) dy = f'(x)dx, c)…

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Q: the following i -7x²+x-

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A: Given query is to find the conic form.

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A: The given function,   f(x)=5xlnx

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Q: Find the solution of the equation, using homogeneous equations. dy/dx = 2y-x+5/2x-y-4   NOTE: To…

A: To solve the DE.

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Q: ator of a sphere, parameterized by spherical coordinates 0, and p. Let "north" point to the top

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Q: Q1. Determine the Inverse Laplace Transforms: 45-4 a) 1 [ (542) (5²74) ] 1) 1 [ 21 g (5 +10)]

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Q: Find sin 0 and cos 0 if tan 0 sin = 3/5 sin = -3/5 sin = 4/5 sin = -4/5 cos = 3/5 cos = -3/5 cos =…

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Q: LO 5 100 160 500 √√25 O +1 O -1 O +1,-1 None of them

A: We can find the solution as below.

Q: Set-up the integral using vertical element for the volume of the solid obtained by rotating the…

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Q: 4. Determine the CORRECT partial fractions for Ax+B C A. + (x²+9)² (x-3)² A B B. + (x²+9)²(x-3)²…

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Q: If f is differentiable and f'(x)=x³-2x²-x+2, then fis increasing or

A: Given, x³−2x²−x+2=f' We equate the given function to zero for critical points. x³−2x²−x+2=0   Step…

Q: Consider the cone shown below. If the height of the cone is 3 and the base radius is 2, write a…

A: We have to parameterization of  the cone.

Q: TT ind the area of the plane region, 0≤x≤. ≤ bounded by y=sin X₁ X=- 2 O1s.u. 1.111 s.u. S.U. 2 О…

A: We have to find out the area

Q: Using Rationalizing Substitution [√x + 1 dx = y² + 4y + 4in(y-1) + C. express the final answer in…

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Q: X Consider the function f(x) = x²-1 (a) Find the intercepts of the graph of f (if any). (b) Find the…

A: All the subparts are solved below-

Q: ! If 2* ((4x-1)/5) =3 then x = 1 17/8 O 0.1 O -0.1 * 5 100 160 500 25 O +1 O -1 O +1,-1 O None of…

A: We have to find the values of the following equation.

Q: Evaluate using the method of trig substitution 6. S dx √16-x²

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Q: B. By using the n-th root test method, test the convergence of the following series: Σα-Απ n=1 Q.2…

A: Solve the following

Q: Determine cuál de los siguientes vectores es paralelo a = -4i-j+5k 1 5 --21 + 글+24 •j+ K →= -8i-2j +…

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Q: If f(x) = f'(x) = 1 COS :−¹(5x²), find f'(x). Use exact values.

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Q: 3- Determine f"(x).. F(x)= cosx cotx

A: This question is related to differentiation, We will solve it using given information.

Q: 3- Find the length of the curves in Exercises 1-4. x = = (y3/2/3) - y¹/2 from y = 1 to y = 9

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Q: 5. How is -28 can be express as rational number with numerated the number 4? 84

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Q: 5 25 1+2+20+20+ 4 16 64 an = ||

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: f f(x)=√√x²³-6x +12, then what is the derivative of fat x=3? Round to the nearest tenth.

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Q: The volume of a cylinder of height 12 inches and radius 7 inches is given by the formula V = 12π².…

A: We have to slove the derivative