A spring requires 7 J to stretch from 1m to 4 m. An additional 4 J to stretch for 4 m to 7 m. What is the natural length of the spring (in meters). (Round your answer to the nearest hundredth.) Use the Math Editor is needed.

Q: Use the washer method to find the volume of the solid of revolution for the region bounded by…

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Q: • Find the exponential F.S of the signal shown below, then find the trigonometric form. of(t) A 1/2…

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Q: Write 2x (x+1)² constants. completely in the form of partial fractions solving all the unknown + v…

A: Given problem:- Find partial fraction of 2x/(x+1)2

Q: Part b: (**) We consider the function f(x, y) = x sin y - y cos x + X-R y Find fx(x, y), fxy(x, y),…

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Q: Find the indicated limit by using the limits 3f(x, y) lim (x,y) → (a, b) g(x, y) lim (x, y) → (a, b)…

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Q: Find all the zeros. Write the answer in exact form. 2 v(x)=x²³ −5x² + 4x+6 If there is more than one…

A: Find out the zeroes of the polynomial.

Q: Use a sum or difference identity to find the exact value of the expression. tan 75°

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Q: ections at the given point

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Q: Question 12 Find a at time t = 1 for the plane curve r(t) = 4t²i+ 3tj. Round your answer to three…

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Q: x³-y²+z³ = 24.

A: F( x,y,z) = exyz f(x) = ∇f = (yzexyz , xz exyz, xy exyz ) λ∇g =  g(x) = 3x2 , g(y) = -3y2 , g(z) =…

Q: Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y - 4xyz + 6yz²…

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Q: Calculus I Find d^2y/dx^2 for x + y^2 = 3

A: Solving the problem by finding the value of the problem.

Q: If u(t) = and v(t) = , use the formula below to find the given derivative. d[u(t) × v (t)] = u' (t)…

A: Using given formula find derivative

Q: Let g(u) be a function such that f g(u) du = ln (1 + 8u²) + C. Evaluate fxg(x²) dx.

A: This question can be solved using the concept of integration by substitution and definite integrals.

Q: 4. Solve for 1 [(ax)²-b²]³/2 J dx.

A: See this solution in below.

Q: Use a graphing calculator to determine which expression can be used to complete the identity below.…

A: topic- trigonometric identities identities useda3+b3=(a+b)(a2+b2-ab)sin2x+cos2x=1

Q: Solve the following linear system in iled, by using Gauss-Jordan elimination : x - 3y 3x + y 2x + 3y…

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Q: Find the general indefinite integral. (Use C for the constant of integration.)

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Q: A 10​-foot ladder is leaning against a vertical wall​ (see figure) when Jack begins pulling the foot…

A: Here we have to find the rate of change.

Q: Describe the level curves of the function. z = x + y, c = -6, -5, 0, 1 The level curves are parallel…

A: Solution is given below:

Q: For f(x) = (x + 1)²-3 where x > -1, find: a. The inverse function, f-¹(x) b. The domain of f-¹(x) c.…

A: Given f(x)=(x+1)2-3 We know that, A function g is the inverse of function f if for y=fx,…

Q: 6. Σ(-1)n-1 sin (2) n=1

A: Explanation of the answer is as follows

Q: 4. y = 2x + 2 - 2x² + x + 6

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Q: Evaluate the following integral using the Fundamental Theorem of Calculus. Discuss whether your…

A: We need to choose correct option.

Q: 5. y = 8x³ - 1 3 4 x 2 - 1 -

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Q: If z = -4xe³xy and x = √t, y = . Then, the value of dat t = 8 is equal to 3√2 (-1/2² + 2³/1) e + ² 4

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

Q: Find the total differential. z = 8x4 8x4y10 dz = (No Response)

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Q: Find the total differential. z = x cos(y) - y cos(x) dz = (No Response)

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Q: Choose all critical points of the function f whose gradient vector is Vf(x, y)= O None of the others…

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Q: Find all values of x and y such that fx(x, y) = 0 and f(x, y) = 0 simultaneously. f(x,y) = 2x³ 14xy…

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Q: Let S be the plane with equation 2x - 3y + 4z = 1. Find parametric equations of a line that goes…

A: Explanation of the answer is as follows

Q: Use the cylindrical shells method to find the volume of the solid of revolution for the region…

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Q: Find both first partial derivatives. = In ( + ) əz əx əz ду || = Z (No Response) (No Response)

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Q: dy x+y=x²y² ln x dx

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: Here, the given curves are: y=1+2x, y=2+x2

Q: What is the area of the region between y=x²-2x-3 and the x-axis from to 6? x=0

A: Area bounded by the curve fx=x2-2x-3 and x-axis on interval 0, 6

Q: Given sec 8- -13 $ 3 03 N what is cos?

A: Solving the problem by finding the value of Cos.

Q: (x³ + xy² + y)dx + (y³+x²y + x)dy = 0

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Q: 2x + 2 6x³ +5x² - 4x y = 3

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Q: Multiply and simplify. (1 + tan ß)² (1 | + tan ß)² = [ (Simplify your answer.)

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Q: The rate of change of N is proportional to 20 + N(x), where N < −25. N(0) = 10, and N(2) = 25, find…

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Q: 8. n=1 (−1)n-1 n². 2n (error] < 0.0005)

A: Solve by adding partial sums

Q: Solve the differential equation by variation of parameters. 1 7 + ex y(x) = = y" + 3y + 2y =

A: The given differential equation is;  y''+3y'+2y=1/(7+ex).

Q: I wrote the same answer and still got it wrong, why did I get it wrong?

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Q: a. A rectangular pen is built with one side against a barn. If 200 m of fencing are used for the…

A: As per the guidelines we are supposed to answer only first question and rest can be reposted..

Q: Identify the surface represented by equation: 9x^2 + y^2 - z^2 + 2z -10=0

A: Given :9x2+y2-z2+2z-10=0

Q: Prove the identity. tan 0 1+ tan ²0 2 sin 20 To verify the identity, start with the left side and…

A: Basic question of trigonometry.

Q: Find the points of inflection of the graph of the function. (Round your answers to three decimal…

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Q: Use the half-angle identities to evaluate exactly. sin 112.5° sin 112.5° = (Simplify your answer.…

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