Evaluate the following integrals. 4x545 2. 3. fx Vr? - 4dx 4. S(2- sin 4r) dr

Q: Test the series for convergence or divergence. 3 3 3 11 3 3 10 12 13 O convergent O divergent

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Q: Given the equation dx + xydy y? dx + ydy. Solve for the solution when x = 3 and y = 0 1. ( ) da + (…

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Q: The solution y, of the homogeneous differential equation y() + 36y" = 0 is O None of them O c_1+c_2…

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Q: Find the nth term of a sequence 2,5,10,17,26, ...

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Q: Express the limit as a definite integral on the given interval. -Дх, [1,4] (x;)2 + 9 lim i = 1 dx

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Q: the differential equation (x+y)dy+xdx=o i separable equation C exact equation C

A: We are asked to find whether is exact or separable or  homogenous equation.

Q: Arcsin(x/y) = 4x + 3y %3D

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Q: If Ax) = Vx -1 and g(x) = x+ 1, which expression is equal to fAg(x))? 1+ー1 Wx²+2x (x + 1) - 1 ベズ+x-1

A: Solution:

Q: P1: |x? cos-1 x dx X* cos

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Q: Solve the second derivative(y") of the following

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Q: Find the equation of the tangent line at the given point on the curve. xy? = 36. (1,6) The equation…

A: This question is related to equation of straight line, we will solve it using given information.

Q: Q5: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given…

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Q: A test has multiple choice questions with 3 choices for each answer; only one answer is correct for…

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Q: y = x* Inx dy : =x³ +4x° Inx dx O Op tion 1 None of these dy - -x -4x° In x dx =x² -4x° Inx dx O…

A: Explanation of the answer is as follows

Q: The Cartesian equation, x = - 4, is equivalent to the polar equation, O. 4 cose Or2 = 4 cos e %3! I…

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Q: The position of a point at time t = 1 is (2, 4) and velocity of the point at time t is . Wha the…

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Q: What is the solution of D.E y" – 2y' = e*sinx when solved using the method of undetermined…

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Q: Q2/ Find the second derivative of the following: 1. 2 Va 2. (x-1)(x2-2x)

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Q: 8. (y- 2x)dx - x(1- xy)dy 0 Ans.

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Q: 12 Indicate a general rule for the nth term of this sequence. 6m, 3m, 0, -3m, -6m, . . . a n =…

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Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent.…

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Q: Find lim f(x). Im f0) -O x-2" X--2" (2.4) (4.3)

A: solution:-left hand limitlimx→2-f(x)=0

Q: Using the Nth term test for divergence, 00 n 5n-2 n2 n=1 diverges since lim V5n-2 n² is equal to O 5…

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Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

A: Here we have to find the surface area of a plane.

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

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Q: In Exercises 1 through 4, find the area of the shaded region. 1. y= Vx

A: Area

Q: For some constant a, the following improper integral a | (x2 + 1)e2×dx 2х converges to converges to…

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Q: Using decomposition into partial fractions, 4x2 + 2 -dx x(x² + 2) is equal to In|x (x² + 2)| + C…

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Q: Find the right-hand Riemann Sum, with three sub-intervals indicated by the table. Hours 7. 8.…

A: We have to find the right hand Reimann Sum.

Q: Use the Comparison Test to determine whether the series converges or diverges. 4n 4n 5n3 + 5…

A: We have to find convergency

Q: 4 Which of the following is the correct expansion of (3x - 3y)2? 9 x2 - 18 xy + 9 y2 9 x2 - 9 y2 9…

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Q: The integral 2 X dx | - Vx2 – 4 3 1

A: The objective of the question is evaluate the definite integral.

Q: Activity 1. Match the functions in Column A with their corresponding antiderivatives in Column B.…

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Q: 2. A bushfire spreads with burning area according to the following function, A(t) = 160t – 40t2 (in…

A: Let's find.

Q: 6 Find the sum of the arithmetic series, 3n+2. 50 75 100 25 O O O

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Q: 4. State and prove the law of sines in triangles. 5. Prove lim,0 V2r + %3D 6. Figure out the…

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Q: 1 is convergent or 1) Use the Integral Test to determine whether the series divergent. ' (3n– 1)?…

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Q: Find a series solution about the ordinary point 0 of the differential equation y"+8xy'-4y-0 O None…

A: Given

Q: re' dy + +1 dr =0 O (y – 1) e + + In z = C 2. O-(y+1) e + Ine =C 2 O (1- y) e + 1. O 2y - e + +In=C

A: To solve given differential equation

Q: The indicial equation of the differential equation x²y" + (x2 – 3x)y' + 3y = 0 about the regular…

A: Given

Q: Solving by variation of parametery"-4y' + 4y = xe2x, the value of Wronskian W is: xe^4x O None of…

A: We can solve this as follows:

Q: Find the x-intercepts(s). if any, of f. (Type integer values, separated by commas.) x=0 (6, 2) (-2,…

A: We need to determine x-intercepts.

Q: 3 2 - VX dx x² – 4 1 2]

A: ∫12xx2-43dxLet u=x2-4.=∫-3012u3du=12·∫-301u3du=1232u23-30=12--123· 323·32=-3-123· 3234

Q: Solving by variation of parameters y" + 2y' + y = e*the general solution is: c_1 e^(-x)+c_2…

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Q: f(x) is a functicn given by Icosxl Assume that floe) find the pourier Series for of fe).

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Q: Determine whether the series is absolutely convergent, conditionally convergent or divergent. Please…

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Q: The general solution of the fourth-order differential equation y() + y" + y" =0 is: %3D y=c_1 +c_2…

A: The general solution of the fourth-order differential equation.

Q: Find T(v) by using the standard matrix and the matrix relative to B and B'. T: R2 → R2, T(x, y) =…

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Q: The solution of the Ordinary Differential Equation 4y" - y' - 3y = 0 if y(0) O and y'(0) %3| 7 - is:…

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Q: Solving by variation of parameters y" – 3y' = x the general solution is: None of them c_1+c_2…

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