A) Find the following integrals: 1) tan-¹(x) dx 1,5₂) 5. DYE

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A: given limit

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Q: y = x(x-2)

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Q: Find the derivative of y with respect to x. y = In (5x)

A: given         y=  apply differentiation with respect x

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Q: Evaluate SS √1 + x² + y² ds where S' is the helicoid: r(u, v) = u cos(v)i + usin(v)j + vk, with 0 ≤…

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Q: 1. Find div F and curl F if F(x, y, z) = 8e™ i − 10 cos y j + 10 sin² z k. div F= curl F=

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Q: 3. Consider the function f(x) = 2x² x+1 (i) Use the limit definition of the derivative to compute…

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Q: can u please solve part (d)?

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Q: Find all values of I where the given series Converges har 3x (x+¹) X+6

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Q: Find the areas bounded by the indicated curves y = 8-2x^2, y=0 Show step by step solution and…

A: given the curves y = 8-2x^2, y=0To find: area between these curves

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Q: Use spherical coordinates to find the volume of the solid within the sphere √√x² + y², and above the…

A: Region bounded within the sphere x2+y2+z2=9 outside the cone z=x2+y2, and above the xy-plane.

Q: Solve. -4. y' = 4y 4; y = 5 when x = 2

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Q: Find Vw. w = xey sin 3z NOTE: Give your answer in unit vector notation; that is, in terms of i, j,…

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Q: Suppose the daily supply equation for noise cancelling wireless headphones is given by P = S(x) = 70…

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Q: 4 Use implicit differentiation to solve for y' if r4y2 - x³y + 2xy³ = (Show your work)

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Q: Determine the boundary limits of the following region in space to set up a triple integral and…

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Q: secxdx

A: I=∫sec2x dx

Q: Evaluate the following limits. If needed, enter inf for X and -inf for -. lim X→∞ lim X118 12x² e9r…

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Q: Find f'(x) if f(x) = tan-1 2x sec²(x) 1 1+x² 2x 1+x² 2x 1+x¹ 2x 1+x² 1-¹ (x²).

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Q: 1. Determine whether the statement is true or false. If it is true, explain why. If it is false,…

A: To determine whether each of the following statement is true or false.(a) If  is any constant…

Q: 8 Two people start moving from the same point. One travels south at 6 miles/hour and the other…

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Q: Test the series for convergence or divergence using the Alternating Series Test. (-1) +1 √n +6…

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Q: 4. Setup an integral expression for the perimeter of the ellipse x² 3 Hint ds = x' (t)² + y' (t)² dt…

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Q: Problem 4: Let en = 2.4-6 (2n), the product of the first n positive even integers. Use the Ratio…

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Q: Evaluate the limit lim x+1 A. 0 B. 3 C. 8 D. Does not exist x-1 √√/x √x-1

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Q: Use a double integral to compute the area of the region bounded by y=x², x=y-2

A: Compute the area of the region bounded byy=x2, x=y−2

Q: a. Find T(t) and N(t) at the given point. x = e cost, y = e sint, z = e; t = 0 T(0)=

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