I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. 2x³+2x²+2x+6 1. Lim X→2 x³+4x+3

Q: The triple integral ¹²-x² √4x²-y x dzdydx is equal to 0.33 0.08 None of them O

A: Let's evaluate given triple integral.

Q: = 4 R is the region bounded by y = x², y = 4x - x² and the line x = and it is revolved about y = 0.

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Q: Using Trapezoidal method √²³x² dx for n = 4 is equal to

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Q: Integrate the equation using the method in trigonometric substition

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Q: ind the general solution of xdy + (3xy + y - e-³x) dx 0

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Q: Find the average value of the function f(x, y) = xy over the triangle with vertices (0, 0), (1,0)…

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Q: Evaluate each of the following line integrals. cy²sin³x √1+ cos²x ds where C: y = sin x going from…

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Q: 9. What is the general solution for the differential equation y"" - 3y' - 2y = 3x? A. y C₁x +…

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Q: The general solution of (D²-2D+1)y=2sin x y=C1eX + C>XeX + sinx By=c₁еx+c₂xe* +2sinx Cy=c₁еx+c₂xe* +…

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Q: A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.  How fast does the tip of…

A: Given that, A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.

Q: The function is X 2 = y² What is 8²% მ2 Y x²

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Q: 7. Find the area between f(x)=-x² + 4x and g(x) = x² - 6x +5 over the interval 0≤x≤1 Ei..

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Q: The reverse order of 4 So Say ex² dxdy is equal to e-1 8e None of them

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Q: d²y dy Consider the differential equation +9y = 9x + 3. dx² dx (a) Find the general solution. (b)…

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Q: Which of the following CANNOT be solved by method of undetermined coefficients? 1 A (D²+1)y: cos X B…

A: Let's find.

Q: Written Activity Related Rates Expanding Rectangle The length of a rectangle is increasing at a rate…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: If x = t² and y = t³, then y O t O o O 3/4t O 3/t O Other: =?

A: In this question, we have given the values of x and y in the form of the variable t and we want to…

Q: General solution of (x²y³ - 11) dx (x²y³²) dx + x³y²dy = 0 1+9x², General solution of dy = tan²(x +…

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

Q: Q9. The Laplace transform of the function u: [0, ∞o) → R (t−2)² + (t− 2) sin(5(t-2)), u(t): can be…

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Q: Solve the following y" - 3y' + 2y = 2x2 + ex + 2xex + 4e3x -

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Q: Integrate the following using Partial Fractions. x dx 1. S x2-3x-4 dr (x²-4)² 2. S

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Q: must

A: When a curve changes from concave down to concave up or concave up to concave down , that means…

Q: lim (lnx) = . x →+∞

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Q: 02/Use the l'Hopital's rule to find the limits in t3-4t+15 a) lim t--3 t²-t-12 X-8x² X-00 12x²+5x b)…

A: Given problem:-

Q: 1. S In(x+2) 2x+4 dx

A: Given,∫lnx+22x+4dx

Q: 1 Lim x→0* x0x 1 sin x

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Q: Find 4-¹, if A = [3 3 O ] 3 -2 0 O [32] −3 0 - [²2] O −3 12 -=[ 132] -3-2 O 2 3 3 2

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Q: 15. The piecewise function -t+ 0 ≤ 2 can be expressed in terms of a Heaviside function as:

A: We are given a piecewise function  f(t) =-t       0≤t<1t2+1      1≤t<2-3               2≤t…

Q: How far does the car travel during that time? * Onone of the choices O260.133 ft O 300 ft O258.133…

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Q: Find the following improper integrals a) Ꮭ -dx 1 x2+x ex b) fodr dx e2x+3

A: We have to solve the given improper integration

Q: 1. f In(x+2) dx 2x+4 2. fx² ex dx 3. f tan³x dx 12

A: We know that integration of xn is xn+1 /n+1. And integration of 1/x is lnx +c.   Here i attached the…

Q: 1. The Maximum point of y=

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Q: For questions no. 2 and 3. Given: A thermometer reading is 60°F at 3:00AM and a Civil Engineering…

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Q: ? Question af Use Mathematica to find the other partial derivative for the function dx f(x, y) = x²…

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Q: 15. The piecewise function -t+ + 0 st < 1 f(t) = ²+1 1st <2 -3 t22 can be expressed in terms of a…

A: This is a problem related to heaviside function which is also known as step function. Based on the…

Q: 12. Find the first and second derivatives of f (x) at x = 1.2 and x=2.0 from the following table 1.2…

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Q: 1 Lim x-0* x 1 sin x

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Q: General solution of = dx tan²(x + y)

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Q: Find ²2 of z = In(xy) 8²y

A: Given: z=lnxy   As we know that; The Power law; ddxxn=nxn-1 The Chain Rule: fgx'=f'gx·g'x And…

Q: (2x³-9x²+2) dx from x = 6 to x = 11

A: Given: ∫2x3-9x2+2dx   from x=6 to x=11

Q: Numerical Integration: •2 1 [.. -dx Jo √x 1.

A: Numerical integration

Q: 2. Use the disk method to determine the volume of the solid obtained by the revolving the region…

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Q: it was estimated that constructing a fence for a project could be done by 11 workers in 15 days. at…

A: Let 'n' be the number of workers. Let 'd' be the number of days required Let WT be the work done…

Q: Numerical Integration: r2 1 S² = = X 0 1. dx

A: Please find the solution:-

Q: The general solution of (D³+4D)y=0 is Ay=e*(c₁cos2x+c₂sin2x) B y=c₁+c₂cos2x+c3sin2x Ⓒy=c₁еx+c₂e²x +…

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Q: Determine the derivative -d/ 4 8 +³−1 - 17x y= y = 25 x-5 x+6

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Q: IV. INDETERMINATE FORMS Show if the following limits produce an indeterminate form. Then, evaluate…

A: The objective is to evaluate the limit.

Q: Find x/2 x-3 lim 148 x+1 O limit does not exist e^-2 Oe^-4 0-2 O-4 O Other:

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Q: дz дz Givenz = xey +yex, Find дх’ду

A: in partial differentiation , other variable is considered as constant when function is…

Q: 2. Simple Chemical Conversion Radium decomposed at a rate proportional to the quality of radium…

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