Find the following limit. 3x²-1 lim

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A: Given:        fx,y=arctanyx , 2,-2     fxx,y=∂∂xarctanyx                   =1yx2+1∂∂xyx taking y as…

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A: Limit

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A: Sketch the plane curve

Q: 7) Solve the equation 2x²-3x-2 x+2 = 0 for x.

A: Given data÷ Solve the equation÷   2x2-3x-2x+2=0

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A: Topic = Differential equation

Q: 3 [(1 + 5a)'di

A: Solve the integral

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Q: Which of the following shows the simplified function of cscxsin 01 -1 tan x O cotx

A: Topic - Trigonometry We are given, csc x sinπ2-xWe know that,sinπ2-x=cos(x)

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A: Topic = Integration

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A: Let's find absolute maximum and minimum value.

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Q: A tank contains 70 kg of salt and 2000 L of water. Pure water enters a tank at the rate 6 L/min. The…

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A: Given: So,           x2+y29-z2=0 and which is an equation of elliptic paraboloid.

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Q: What is the range of the function f(x) = = x + b -, a, b = R and a, b =0? xa

A: range of fx=x+bx-a

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A: We can evaluate the definite integral .

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A: We can find solution sets.

Q: Suppose that the length 7, width w, and perimeter P of a rectangle are differentiable functions of…

A: Topic = Derivative

Q: 1. Consider the DE d'y dx2 - 2 dy − 3y = −9x − 3, y(0) : (0) = ² – 1. - dr Verify that y =…

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Q: Find the second derivative of the vector-valued function r(t) = (7t + 5 sin(t))i + (4t + 5 cos(t))j…

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Q: Consider the initial value problem y" +36y=et, y(0) = yo, y'(0) Suppose we know that y(t) → 0 as…

A: The given differential equation is: y''+36y=e-t Boundary conditions are: y0=y0  ,y'0=y'0yt→0  as t→∞

Q: Find the slope of y= 1-x x² +1 at x = -4.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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Q: Below are the polar coordinates. Find the Cartesian Coordinates. (0,5) (-5,0) (0.-5)

A: The polar coordinate is 5, 3π2 We have to convert the Polar coordinate to cartesian Coordinates.

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A: Given query is to find the time where velocity is 25.

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Q: Find an equation of the tangent line to the function y = 2x² at the point P(1, 2). Solution We will…

A: We need to find an equation of the tangent to the function y=2x2 atthe point P1,2.Note: We will…

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Q: Evaluate the series or state that it diverges. Σ (3) 8 k=2 8 3k Select the correct choice below and,…

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Q: 2 x dx + y(x - 1)dy = 0, @x=2, y =1

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Q: Consider the initial value problem Suppose we know that y(t) → 0 as t→∞o. Determine the solution and…

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Q: 12. D(x): = 1800 Vx+1 S(x) = 2√x + 1

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Q: Determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a…

A: A sequence an is said to be monotone if it is either increasing (i.e., an≤an+1) or decreasing (i.e.,…

Q: If f(4) = 13 and f '(x) ≥ 1 for 4 ≤ x ≤ 7, how small can f(7) possibly be? Need Help? Read It Watch…

A: See this solution in below.

Q: > 9:37 A particle moves along the x-axis so that its position at time 0 < t < 18 is given by x(t),…

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