Q5 a) 100 5² +2³+ [In(Inr)] lim 1+ 7 +6² + [In (In x)] 200 cos x ln(x - *) *-+*+ In (e² - e*) b) lim

Q: improper iterat 1/x3 y dy dx

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Q: Step To sketch the graph of f(x) = 4x - x², first construct a table of values by evaluating the…

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Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y,…

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Q: Write the vector shown above in component form. Vector = Note: In the graph, each box is 1 unit by 1…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Determine whether f(x) approaches or as x approaches 6 from the left and from the right. f(x) = sec…

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Q: Verify Green's Theorem by evaluating both integrals (ON-OM) d [[ y² dx + x² dy = √ √ ( ³x for the…

A: In this question, we want to verify the green's Theorem for the given integral.

Q: y = e²+3 dy dx Find dy dx Type sin(x) for sin(x), cos(x) for cos(x), and so on. Use x^2 to square x,…

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A: The linear operator that annihilates anxn+an-1xn-1+....a0 is Dn+1 The linear operator that…

Q: Sketch the solid region whose volume is given by the iterated integral. [³ O √,2-4 Evaluate the…

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Q: Describe the transformations that map the function y=2^x on the function y=2^x+3

A: Solution

Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: Given general solution of the equation y=C1e-4x+C2e-2x

Q: If a company spends r million dollars on research, it sales will be s million dollars, where r and s…

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Q: Use Green's Theorem to calculate the work done by the force F on a particle that is moving…

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Q: 8 -6 4 수 +

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Q: Find a particular solution to the differential equation Ур = -6y" - 5y'-y = -(t² + 2t + 2e²t).

A: To find a particular solution to the differential equation.-6y''-5y'-y=-t2+2t+2e2t

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) Jx x5/2 In(x) dx

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Q: Evaluate the iterated integral. 2 . (x+y+z) dx dz dy

A: The given integral is: I=∫02∫08∫01x+y+zdxdzdy   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: Which of the following planes is normal to the line given as: x = 2t + 3, y = 5t - 7, z = t - 4 O a.…

A: This question is based on dot product.

Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

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Q: The population density of a city is approximated by the model f(x, y) = 2000e-0.01(x² + y²), x² + y²…

A: This is a problem related to double integration. Please follow the general procedure given below.

Q: A force of 540 newtons stretches a spring 3 meters. A mass of 45 kilograms is attached to the end of…

A: A  force 540 Newton stretches 3 meters .a mass of 45 kg  is atteched to the end of the spring and is…

Q: If f(x) = f'(x) = f'(4) = 4x + 7 2x + 3 find:

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Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz²j + 4yz²k; (3,…

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Q: 000 is budgeted for production of the product, determine how that amo ion will be maximized when…

A: We are asked to find the maximize the profit

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: Evaluate the following Rational Fractions -(3 cos² 0 + 8 cose-12) sin 0 de cos³ 0+7cos² 0+ 12 cos 0…

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Q: Tutorial Exercise Consider the differential equation x²6xy +10y=0; x², x5, (0,00). Verify that the…

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Q: Find F as a function of x and evaluate it at x = 2, x = 6 and x = 9. = $₁² F(x) = F(2) = F(6) = F(9)…

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Q: Find the general solution of the given higher-order differential equation. y"" - 8y" - 9y' = 0 y(x)…

A: The given differential equation is y'''-8y''-9y'=0 ............ (1)  Equation (1) can be rewritten…

Q: Determine the general solution of the given differential equation. y"" - y = 11 sint NOTE: Use C₁,…

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A: Given 16y''-40y'+25y=0

Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x - y)dy

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Q: If z = 5x2 + y2 and (x, y) changes from (1, 2) to (0.95, 2.1), compare the values of Δz and dz.…

A: We have to compare the values of Δz and dz.

Q: 5. The sum of thrice a number and two equals 6 less than four times the number. Find the number.

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Q: -10 -10 10 (c) Describe the relationship between the graphs. The graphs off and f" are reflections…

A: Let's solve for c part.

Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. 8u, y = uv x = UV a(x, y)…

A: Given,            x=uv-8u , y=uvTo find : Find the Jacobian ∂x,y∂u,v for the indicated change of…

Q: The rate of change of revenue (in dollars per calculator) from the sale of x calculators is R'(x) =…

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Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. - 1/2 (u = v), y = 1/2 (u…

A: Jacobian ∂(x,y)/∂(u,v)= ∂x/∂u* ∂y/∂v - ∂y/∂u* ∂x/∂v

Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: Use the equation Σ x" for [x] < n=0 (Express numbers in exact form. Use symbol 6 1 - x4 Σ 1 1-x Σ…

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Q: Find the smallest number n of terms needed to obtain an approximation of the series 10 -6 n = k=1…

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Q: 1. Sketch the graphs of x = 6y-y² and x = y² - 8. Shade the region bounded between the two curves.…

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Q: f(x) = (x-1)^3 (x-1) (x-2)

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Q: TT/4 0 tant di

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Q: Three different forces act on an object. They are: F₁ (8,5) (1,7) F₂ F3 (0, 3) = - = Find the net…

A: The three forces are given as: F1→=8,-5 F2→=1,7 F3→=0,3

Q: Use cylindrical coordinates to find the mass of the solid Q of density p. ₂-(+² x² + y² ≤ 16, x ≥ 0,…

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Q: 1 3. How many terms of the convergent p-series k=1² must be summed to obtain an approximation that…

A: We have to find no. of terms of the convergent p series.

Q: Use Newton's method to approximate the indicated root of the equation correct to six decimal places.…

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Q: 16-1

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