Use limits to identify all the linear asymptotes of r³ - 3x - 1 x² f(x) = 2x² +1 x² + 2x +1' x < 0 x ≥ 0.

Q: Find the values of a and b such that the following function a² cos(x − 2) — 26(³-x), if x 2, is…

A: Topic = Limits

Q: 3. ) Consider the function f(x, y) = 2r+y²-2²-2y. The critical points of f are (-1), (0, 1) and…

A: In this question, we need to classify each critical points using second derivative test.

Q: use Green's Theorem to evaluate the f(x² - 3y) dx + 3xdy where C is a circle x² + y² = 4 and…

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Q: A) Evaluate the following integral dx (x - 1)(x-2)(x − 3) - , 10 points

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Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

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Q: 121+ 18 + bh + S2 + b fl

A: We can solve this as follows:

Q: Verify that f has an inverse function. Then use the function f and the given real number a to find…

A: Given problem:- Verify that f has an inverse function. Then use the function fand the given real…

Q: State the order of the given ordinary differential equation. (1-x)y" 5xy' + 7y = cos x Determine…

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Q: R = {1,2,3,4,5,6} and S = {2,4,6} is set S a subset of set R?

A: R = {1,2,3,4,5,6} and S = {2,4,6} is set S a subset of set R?

Q: (x) + Find the general solution аху- х+у о у-xlncxЈtc 2 x² Ў= х²-хутуг у-х- х Нихте з y = x + y + y…

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Q: Verify that the indicated family of functions is a solution of the given differential equation. A dP…

A: Given  dPdt=P1-P;   P=c1et1+c1etTo Find: We need to verify the solution

Q: 3- prove that w = w yx if w = xy² + xy +

A: Given problem:- w=xy2 +x2y3+x3y4  Prove that wxy =wyx

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: B 1. Find the eigenvalues and eigenvectors of A = 3 linearly independent? Why? -2 -3). Are the…

A: This is a problem related to matrix operations. Based on the general formula and concept we will…

Q: C-the derivative is y = 0³ e 28 cos 50

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Q: Q2)Evaluate the following integrals in (3) 1- dx 3.x²

A: SOLUTION-

Q: 1. Evaluate √2 √4x² dx using a trigonometric substitution.

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Q: lim 1-0 ان sin 1² t

A: Given limt→ 0sint2t

Q: Q3- Use Green theorem to evaluate [7y-ex]dx+ [15x-sin(y³ + 8y)] dy Where (c) is a positively…

A: This is a application of integral problem

Q: Which of the following is the appropriate substitution to evaluate the given integral using…

A: This question is related to indefinite integration, we will solve it using given information.

Q: fcx) = sinh x X il 10 - 2 (1+X+X/21 + X/31 + -)-(1-X + X²/21 - X/31 --) 2 3 +2 5 2x+2 31, 2 3! 51…

A: We know, coshx= [ex+e-x]/2 and emx=1+mx+m2x22!+m3x33!+... for any real number m

Q: Evaluate the following - ² (x − 1)(x − 2)(x-3) integral

A: Given problem:-

Q: find: Seos nit dt findo S sinnat at

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Q: 2. -) Consider the surface x² + y²-2xy-x+3y-z=-4 at the point Po(2, -3, 18). Determine the…

A: Let's find equation of tangent plane and parametric equations of normal line.

Q: Answer: y = -√2 sin x + 3 # Find the particular solution, y = f(x), to the differential equation dx…

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Q: What are the domain, range, and period of the function f(0) = -2cos = -2cos ( - - - 0) + 1₂

A: Let's find domain and range for given  function.

Q: The result of dy/dx for the following function is COS X y = 1+sin x

A: In this question we have to find the differentiation.

Q: Q5) Solve the following using Trapezoidal rule with n6 f(x) = f*xinx. dx

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Q: (A) Find the slope of the line that passes through the given points. (B) Find the point-slope form…

A: Solution

Q: smal 150 125mxa 081 dia! 3a. Find the coordinates of the relative maximum and relative minimum of…

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Q: Note: Answer All the Questions 01- Fill in the blank for the following statements 1- The cylindrical…

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Q: The area of the region between the x-axis and the graph of the function shown below and the lines…

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Q: The Value of the integration for the below function shown is : I se sec²2xdx

A: See the details solution in below

Q: let X be a random variable with density function given by x si -1≤x≤1 f(x) = ={1 0 en otro caso x…

A: As the given function is triangular function between -1 and 1 , hence, we can use the general…

Q: 5. Use the Squeeze Theorem to evaluate lim sin z 2 1-00

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. (x)…

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Q: + 192t +9. Find its maximum height. - 16t²+ The height (feet) of an object launched in the air t…

A: Second Derivative Test: If x=a is a critical point of the function f(x) and f''(a)&lt;0 then f(x)…

Q: 15 //dx Sº

A: Topic:- application of integration

Q: When a factory operates from 6 AM to 6 PM, its total fuel consumption varies according to the…

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Q: QUESTION 2 1. The sketch shows x)- asinx for [-90%,270"] 31 1.1 Determine the value of a 1.2 Sketch…

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Q: 3- show that the diff. equ. is homogeneous and Salve it (2x+34) dx +(y-x)dy = 0

A: To solve the given differential equation

Q: Q1 Find the value of x, y, z if the matrix 0 2y Z A = X y -Z x -y Z satisfy the equation ATA = 1. 6…

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Q: which means that and thus 2x 5x + 3 and g(x)= and g'(x) = D II 5x + 3

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Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

A: Here we need to solve the given differential equation.

Q: Find the integral which represents the total mass of the triangular region below (see the picture),…

A: Total Mass = ∫∫R δ dA ; where, 'δ' is the density . Note : As per our Guidelines , we can solve…

Q: 2.1) Choose the correct answer for the following: has: a) 3rd order and 2nd degree c) 2nd order and…

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Q: x Cos y Q7. Let f(x, y) = ye ²x + Find fxyx (0,1). √√y² +1 dy dz Q8. If z = x² + 3y, x = sint and t²…

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Q: y = ln (sec (ln 0))

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Q: 1505 152 maxa 081 din 3a. Find the coordinates of the relative maximum and relative minimum of the…

A: Solve the following

Q: Solve the differential equation: dx ||

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