Evaluate the line integral [ z²dx + x²dy + y²dz, where C is the line segment from (−1, −1, −1) to (1, 1, 1).

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A: Limit at x tending to -5 exist and equal to 5 . At x = -5 f(x) is not continuous.Explanation:Step 1:…

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Q: Find the exact length of the curve. x = et - t, y = 4et/2, 0 ≤ t≤ 3

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Q: Exercise: Solve the equation d³y dx3 +3d²y dx² dx +30 + y = 0

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Q: 3) An adult human at rest inhales and exhales approximately 520 ml of air (called the tidal volume)…

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Q: Use logarithmic differentiation to find dy/dx.

A: Answer is given below Explanation:

Q: Find the length of the indicated portion of the curve. r(t) (3e cost) + (3e sint)j+3e'k. - In4sts0…

A: Given:To find:The arc length is calculated as-

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Q: 8. Sketch the graph of the function with por and vertical asymptote at x=1 and horizontal asymptote…

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Q: Verify the identity. sin 160 4 cos³40 sin 40-4 sin³40 cos 40 Statement sin 168 Rule Pythagorean

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Q: Find the area of inside = 22cose and outside = 11 by sketching the graph of the equations using the…

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Q: b) y = (3x-1)e-x²

A: The equation you've provided is a mathematical expression in terms of a variable x, given by:…

Q: Suppose that  f(x) = 10x − 7 ln(x),      x > 0.  (If an answer does not exist, enter DNE.) (a)…

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Q: Example 1: z=x³y_x=2t and y=t² Find dz dt

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Q: 2) a) Write the following curves in parametric way z(+) = x (H)+ight) 1) zz + i (z-7)-2=0 is) Im ( 2…

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Q: A. Find S'(t) B. Find S(20) C. Find S'(20)

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Practice

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Q: Rewrite the following iterated integral in the order dy dx dz: f(x, y, z) dz dy dx.

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Q: 11-X2 0 dx x = Sin O the trig aluate using the bstitution x=Sino

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Q: Check all of correct statements about differentiable functions. The derivative of the sum of two…

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Q: let f(x) = In (1+x). find second degree taylors polynomial centered at x=1 for f(x): f" T₂ (x) = f…

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Q: Sin U X-4 Compute using *3-8x+7 Partial fraction decomposition. what is another method that can be…

A: The value of the integral is21​ln∣x2−8x+7∣+C,where C is the constant of integration.Explanation:

Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have three…

A: Find the local maximum and minimum values and saddle point(s) of the function.

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Q: What is the purpose of hypothesis testing in statistics? a. To determine the sample size required…

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Q: #5 Given r(t) = (x(t), y(t)) = (4 sint, -3 cost- a) Find the tangent vector when "t=to=3π/4 (b) Find…

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Q: Problem #3: Consider the following function. f(x, y) = x3+18xy-912 (a) Find the critical points of…

A: (a):  (c) (0,0), (6,-6)(b): -324,324(c): (E) Saddle point , Relative minimum Explanation:

Q: Find the exact length of the curve. y = ² ²x³/2, 3 0≤x≤6

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Q: 1) Write an equation of a function that meets the given conditions (a) x - intercept: (1,0), (3,0);…

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