Consider the curve given by x³ + y³ = xy² + 1. Find the slope of the tangent line to the curve at the point (1,1). -1/2 3 -2/3

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A: t01234567A'(t)0.910.870.720.670.610.510.480.43

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A: We have to state the domain for the function

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A: We have to Determine the value of integral.

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Q: Let ā = ( – 5, — 4, 5) and - 4, 5) Find the projection proja b 6 and 7 = (3, 1, 0). =< of b onto a.…

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Q: A particle moves along a coordinate axis. Its position at time t is given by p(t) = -t³ + 2t² - t -…

A: Solution-The position function is given by,We know velocity function is given by,

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Q: = 5 = [3, 6, 2] and ☎ = [0, 0, 8], find a unit vector perpendicular to both 5 and 2.

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Q: Determine whether the alternating series converges. k + 1 9k + 1 Σ(-1)²+1, k=1

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Q: Evaluate the integral. (Use C for the constant of integration.) 25dx 25 + ex

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Q: 51. lim x→1 2. / 1 53. lim x-0+ X 1 55. lim - X 1 x→0+ X X - 57. lim x√x x-0+ 63. lim x¹/x x18 - 1 1…

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A: Vector cross Product:If we have a vector , then the cross product of  with itself is:Vector Scaler…

Q: 25. lim √√1 + 2x - √√1 - 4x X x-0018 101

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A: To solve this problem using Lagrange multipliers, we need to define an objective function and a…

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Q: ii. Consider the following differential equation: d²x dx dt² +5+8x = f(x) where f(x) is the input…

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Q: Thanks for answering. That one was correct . Please could you also answer the second one?

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Q: 1. Determine the derivative of each function. (DO NOT SIMPLIFY) a) f(x) = x³5x b) g(x)= Fl

A: Use the quotient and product rules of the derivative

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A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Calculate the integral R f(x,y)dA for f(x, y) = 10-4x²y and R: 0≤x≤ 2, -1 ≤ y ≤ 1.

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Q: (2) True or False: a) Local extrema can only occur at critical numbers.__ b) Everywhere there is an…

A: As per bartleby guidelines only one question is allowed to solve with maximum 3 sub parts , so here…

Q: Evaluate the integral ſ 36-x2 + C 36 dx 2²√36-22 using trigonometric substitution. Note: Use C for…

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Q: Convert the rectangular coordinates of each point to polar coordinates. Use degrees for 0. 5. (√3,3)…

A: By the answering guidelines of Bartleby, We can answer only first three subparts, please post other…

Q: Evaluate. Assume u > 0 when In u appears. # S (In x) 4 dx X

A: Given :- To Evaluate :- The given integral.

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Q: Evaluate the integral. te⁹t dt Step 1 Recall the formula for integration by parts, which states that…

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Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of…

A: As per the guidelines, I am providing the solution to the first question.

Q: Evaluate the following indefinite integral. 3 -dx

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Q: so what is the solution for 23,24

A: The given integrals are;23) √x , limit from 1 to 924) x-2/3, limit from 1 to 8.

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Q: For what value of b does the limit b = exist? What is the value of the limit? b = b b b = = lim x→→2…

A: Limx--2(6x3+5x2-12x+b)/(x2+x-2) Find the value of b and the limit.

Q: Let à = ā ( – 5, — 4, 5) and b Find the projection of b onto a. proja b = (3, 1, 0). V

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Q: 4. lim (9x + 1)² x→-1 In the following exercises (5-10) use direr

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