Determine the intervals on which the function is concave up or down and find the points of inflection. f(x) = 6x³ - 11x² + 1

Q: Find the equation for the line tangent to the curve 2ey = x + y at the point (2, 0). Explain your…

A: Equation of tangent to curve is given.

Q: Evaluate the following integrals: O •(Cartesian to Polar) Given the Cartesian coordinate, find FOUR…

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Q: Əw at = xysin(z2), x= s-t, y=s2, z t². Use the Chain Rule to find .

A: We know that derivatives of d(xn)/dx = nxn-1. And d(sinx)/dx = cosx  Here i attached the solution of…

Q: The graph of a function y = f (x) is shown below. Use the graph to estimate all (there may be more…

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Q: If w=2x² +2y+3z + cost and x-y=t, find the partial derivatives below. w aw Əw a. b. C. dy dy əz X, Z…

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Q: Given R(t) = 4 costi + (1+3cost)j +5sintk. Find || R'(t)||. 5 O 4 O 2 O none of the above

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Q: Suppose that sin(θ)=4/8. What tan(θ)=______.

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Q: Find the general solution of nx dx = (x + 1)² ylnx

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Q: [CLO-2] Evaluate the improper integral. 8 √₁² (0-²x + ₁ 72² 2² ) ₁ dx 1 1+x²

A: Follow the procedure given below.

Q: Find (au/ay), at the point (u,v)=(√2,-2), if x=u² + v² and y= uv. du (Simplify your answer.) ay…

A: Here we using jacobian formula.

Q: (a) Find the general solution of the differential equation d²y dx² +9y = x² + x + 1.

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Q: Find the point (if it exists) at which the following plane and line intersect. - 10x-3y-9z= - 19 and…

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Q: Evaluate lim f(x), f(x) = (3x² + 5x − 1, (7x² - 2x - 3, x ≤ 2 x > 2

A: Topic:-  limit and continuity

Q: L (x − 3)(x + 2) dx – -2

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Q: example I= 1 5² die fex2=212 9=0₁6=1

A: The integration of the integral is x2 limit from 0 to 1.

Q: Find the mass and center of mass of the lamina that occupies the region D and has the given density…

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Q: uate (f¹) '(2) for the function f (x) = √x³ + x² + x + 1. lain your reasoning and write the solution…

A: Topic:- function and its derivatives

Q: The equation of the tangent line to the graph of f(x)=ln|x at x = -2 is v=²(x+2)+n2 (a) TRUE (b)…

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Q: What is the area of the region between X |y=x2–2x−3 and the x-axis from x=0 to x=4?

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Q: Find the particular solution (D² + 4D + 4) y = 0 when x = 0, y = 1 and y' = -1 What is the general…

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Q: Solve the differential equation y""+y" = 3x² + sin x - 2 cos x What is the particular solution?

A: We have to find the particular solution.

Q: Evaluate the following integrals: 4x 6. ²x3x²y²dy dx -TT/3 7. p² sin 0 de dp Jπ/6 S3

A: The integration of the integral is  6) 3x2y2 7) (row) 2sin(theta).

Q: Numbers 10,11,12 please

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Q: Consider the matrices shown below: Find the value of K such that 4 B-B2C-13 = 5 1 10 18 18 B-¹C – 15…

A: Given B=4-102 and C=142315We know that if A=abcd then A-1=1ad-bcd-b-caB-1=18+12104=192104

Q: 15-18. Find the extrema of f(x) = 3x - 4x³ on the interval [0, 2].

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Q: We start from the expression for the contact force 4 a³ 1/21 F=E (₁ 7² - (07*³²¹) ³²) '8γπa3 E* 3 R…

A: We have to find the differentiation of the above equation.

Q: Q1): Prove that: A square matrix B has inverse if and only if determinant of B is not equal zero.

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Q: Given the function below f(x) = √-324x³ + 1053 Find the equation of the tangent line to the graph of…

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Q: r sin ³0 cos³ 8 do 3

A: Topic:- application of integration and trigonometry

Q: 3. Compute f(x)dx 2x f(x) = { 4 if x < 1 if x 21

A: Evaluating the definite integral by splitting the integral at x=1

Q: 1-12 Find the area of the surface. 1. The part of the plane x + 2y + 3z = 1 that lies inside the…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 6. a) Find the critical value(s) of f(x) = x + 2sin(x) on the interval 0≤x≤ 2π 3 b) Classify each…

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Q: Evaluate lim x-0 1-√√1+x X

A: Given problem:-

Q: 10 5-2 sin 8 a. find the eccentricity and identify the type of conic; b. write an equation of the…

A: This is a problem related to polar function. Based on the general formula and concept we will answer…

Q: [4pts] Consider a point in Cartesian coordinates given by (3√/3, -3, -8). a.) Find a corresponding…

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Q: a. x K=I 34 K!

A: We can solve this as follows:

Q: y = ln 1-x² 1+x²

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Q: Find the point on the plane 5x + 4y + z = 11 that is nearest the origin. What are the values of x,…

A: First we find the distance(d) between a point (x,y,z) on the plane and the origin .Then form a…

Q: Consider the following matrices: r 2 2 C# -H -N A = B = 30 1 € 4 1 0 -5_ Perform the following…

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Q: Evaluate the following integrals: 0 (Cartesian to Polar) Given the cartesian coordinate, find FOUR…

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Q: Find the value of the following implicit derivative tan y-sec x=5 find...y'

A: Given problem :- Find the value of the following implicit derivative   tan(y)-sec(x) = 5 find   y'

Q: 5s + 4 83 2t5t³ Option 4 None of the Choices 2t + 5t³ Option 3 Option 1 5t + 2t³ 5t - 2t³ Option 2

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Q: Find the Laplace Transform

A: Topic:- application of integration

Q: cos³ t

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Q: R 쫘 = 0.138 & R" . R₁ " 0.126

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Q: x-1 x-1+√√2x-x²-1 Evaluate lim

A: Please refer to the image below

Q: Find the general solution of the following linear first-order ODE (1-x²)y' +2y-x=2

A: We need to solve D.E.

Q: Compute the general solution to the second order linear non-homogeneous differential equation: d²y…

A: Given differential equation, d²y/dx²-2dy/dx=8sin2x Corresponding homogeneous equation, (D²-2D)y=0…

Q: Q2/Test whether the differential equations are exact and solve those that are. (Answer only two) -y²…

A: We have to solve given differential equation.

Q: Differentiate the following function. f(x) = (x+2) e-6x +1 f'(x) = (Type your answer in factored…

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