Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural length. Find the work required to stretch the spring an additional 3 ft. A 33 foot-pounds B 30 foot-pounds (C) 24 foot-pounds (D) 27 foot-pounds

Q: Find the work done by the force field F(x, y) = x sin(y)i + yj on a particle that moves along the…

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A: the solve volume

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A: see below the calculation

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A: Given; F(z)=Z^3+8/Z^3-Z^2 We have to find final value

Q: 1 m ( x² + 3102=²7) dx x²+3x-7 X-2 Evaluate the integral: Se A +2²2 + — + In|3x-6√ + C Ⓡ X/²2 ₁ B…

A: A detailed solution is given below.

Q: Find the area bounded by : f (x)=e*, g(x) = e¯* and x=3. A (e² + 1)² e² sq. units (B) (e³-1)² e3 C…

A: To find the area bounded by curves

Q: Evaluate the double integral: (A) 40 B 30 C) 60 D) 80 ²(3x² +9y²) dxdy

A: The integration are.  .

Q: * (ارفق الاجابة) The eigen value of matrix 1 -1 O 1+i, 1-i O 1+i, 1+i O 1,-1 11 1-i, 1-i

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Q: (1) [ Evaluate the indefinite integral by substitution: a+bx² dx 3ax+bx3 (2) / sec³xtanxdx T

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Q: Give the domain and range. Then, use the graph to find (a) f(-2). (b) f(0), (c) f Ay 40 & M 2 X and…

A: Answer: The solution is given below:

Q: 腰 √√/XX S₁ Solve the integral: A 3√√√x² + C √√x² (B) + C 6 Ⓒ6√√x +C dx

A: ∫x3x2dxRewrite:=∫1x56dx

Q: X-2 dx Evaluate the integral: Sein(x²+3x-7) A x²+5x+In|3x-6|+C B ++ In|3x-6|+C 2 5 © +²2+5x+In/x-21…

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Q: . Graph each of the given functions and solve for the area of the region that they enclose. 2. 4.…

A: As per the instruction, we will be answering the first one. Graph:

Q: Q1:/ Find the general solution of non-homogenous differential equation using Variation of Parameters…

A: Given problem:- Find the general solution of non-homogenous differential equation using Variation of…

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Q: L₁ |x|dx

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Q: 10. y (e-3x+4 +2)/(e2+3x +1)

A: The given function is ; y=(e-3x+4+2)/(e2+3x+1).

Q: Evaluating A 18 √*1/200 (A) **/2 B √9-x² dx using trigonometric substitution will lead to: cos²0d0 0…

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Q: S dx √4x² - 49 x > 72

A: In order to integrate easily certain assumptions need to be made by using some variables.

Q: 5x+√x 3.y=(x²+1)² 4. Using y = 5x + 3x² + 1, find all the derivatives and evaluate f"(2) f(3) (-2).…

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Q: dy ssuming 5x³ +9y² − 4xy = 0 defines y as a differentiable function of x, use the theorem == dx Fy…

A: Given query is to find the derivative at indicated point.

Q: Verify that * / II 21 ?х ду 224 ду ох - for f(x, y) = 4x4y3 - 6xy5.

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Q: - 1₁₂ (3+√4-2²³) dx -2

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Q: 3x² dx

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A: Evaluating the definite integral

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A: answer is in next step

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A: Solution:

Q: where y is considered to be a function of . In this exercise, you will determine whether or not y =…

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Q: Find Vf at the given point. f(x,y,z) = x² + y² -32² + z lnx, (1,4,5) Vf|(1,4,5) = 7i+ (8)j + (-30)k…

A: Topic = Derivative

Q: 15. Iv X V9 – x2 - dx

A: We want to integrate the given function.

Q: Why is it "h • db/t + b • dh/dt"  instead of   "h • dh/dt  + b • db/dt"?

A: Using Rule of differentiation.

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Q: L²x√x-2dx

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Q: |x-4|dx

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Q: Give the domain and range. Then, use the graph to find (a) f(-2), (b) f(0), (c) f (9) 1 (2) Ay Q 40…

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