The strength E of an electric field at a point (x, y, z) due to an infinitely long charged wire lying around the x-axis is given by E(x, Y, z) = 3 Describe the level Vy? + z2 surfaces of E.

Q: For each sign chart for f. Carefully sketch the graph of both functions f and f. Upload your work as…

A: When derivative of f is positive then f is Increasing and when f' is negative f is Decreasing

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Q: Find curl (2z i + 3x j + 6y k). curl(2z 2z i + 3x j+ 6y k) = ( i )i + ( i j + ( i )k

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A: On solving this we will get

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A: topic- distance between lines

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A: To solve for x using the the given equation.

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A: I have stated the used formula in the solution

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A: given function : f(x)=log3x and g(x)=2from figure it is clear that intersection of both curve is…

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A: Find derivative of position vector then we get velocity vector then put the given value

Q: 6. Consider the DERIVATIVE f' graphed below. Sketch a possible graph of the original function f on…

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Q: Determine an equation for the tangent to the curve f(x) = 2x3 + 6x2 - 2  at x = -3

A: Given query is to find the equation of the tangent.

Q: (c) f''(x) = cos x, f(0) = 1, f'(0) = 2, f"(0) = 3.

A: Explained below

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 7 cos(t)i + 3 sin(t)j+…

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Q: Solve the equation algebraically. Round the result to three decimal places. 3+ln x = 0 8 e-354.598…

A: Using algebra

Q: Find the volume of the region enclosed by z = 1 – y? and z = y² – 1 for 0 < x < 21. V =

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Q: Find the values of c guaranteed by the Mean Value Theorem (MVT) for f(x) = =x + 7 over the interval…

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Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

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Q: 13. Calculate the divergence of the vector field F = x1e1 + 2x1e2 + +nx1en. ...

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Q: Consider the functions. f(u) = u³ + u g(x) = cos (x) Find the following function and derivatives.…

A: The given functions,fu=u8+ug(x)=cos(x)

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Q: Consider the solid of revolution obtained by revolving the region between the curves y=0 and y=x^2…

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Q: a) fx² sec2

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Q: Graph the eauation - include local+ Absolut extreme Points if applicable - -include inflection…

A: maxima minima

Q: Evaluate the limit using L'Hospital's rule: Lim0+1 In(x+1) 2xe"

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Q: +4

A: To check the convergence of the given improper integral:∫-∞2dxx2+4

Q: nvestigate the convergence of the following series. H.V 2n+5n 2) Σ-1 3n %3D1 1LJ!

A: We have to find out convergence

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Q: (9, -7) (3, 1). Find 吕 ロ师仁 ?

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Q: 20. Evaluate the limit lim 213

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 3 cos(t)i + 5 sin(t)j…

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Q: im Y cosx t Zx メナロ0 7x¢ し

A: Given query is to find the limit of the expression.

Q: Find curl (6z i + 7x j + 8y k). curl(6z i + 7x j + 8y k) = ( i )i + ( i )j + ( i )k

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Q: 59-64 Use Property 8 of integrals to estimate the value of the integral. x'dx 60. | Jo x+4 59. dx…

A: ∫xn dx = xn+1n+1 +C ∫tan x dx =ln sec x+C

Q: Consider the matrix -8 A = 13 21 1 4 -2 15, Where a;, represents the entries for A, for i= 1,2,3 and…

A: Given,        -8    0    5 A= 13    21  1         4    -2   15 a ij represents the entries for A,…

Q: A ball is launched straight up in the air from a height of 5 feet. Its velocity (feet/second) t…

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Q: Determine the amplitude, period, midline, and phase shifts of the function. Then write the equation…

A: Given problem:- Determine the amplitude, period, midline, and phase shifts of the function. Then…

Q: Find the particular solution of the differential equation that satisfies the initial condition(s)…

A: topic - differential equation

Q: Find the unit vector in the direction of (3, -2). Write your answer in component form. Do not…

A: We will find the unit vector.

Q: Evaluate the integral. (Use C for the constant of integration.) 2 cos (a) da sin(a)

A: Given query is to find the value of the integral.

Q: Evaluate the line integral / (3x + 9y)dx + (4x – 5y)dy along the curve C : x = 10 cos t, y = 20 sin…

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Q: b) Use L'Hôpital's Rule to evaluate the limit L. e2x lim X→∞ x2

A: We can solve part in the following steps.

Q: Find V · (V × F) if F(x, y, z) = 10 sin xi + 5 cos(8x – 9y)j+ 4zk. V· (V × F)

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Q: Find the global minimum of the function f(x)=2x^3+3x^2–12x+4 on the interval [-4,2].

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Q: Evaluate the line integral -ydx + xdy along the curve C C : y? = 15x from (15, 15) to (0, 0). NOTE:…

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Q: Find V x (V × F) if F(x, y, z) = 4.xyj+2xyz k. ▼ × (V × F) = %3D

A: ∇×F=i^j^k^∂∂x∂∂y∂∂zPQR  for a vector F=Pi+Qj+Rk in terms of x,y,z