п! n4 n=1

Q: dy x+3y. dx 2x

A: First order differential equation :  Consider the first order differential equation…

Q: Find the (2x + 1)³ dx A. (2x + 1)2 +c (2x + 1)3 + c 8 С. (2x + 1)4 + c D. (2x + 1)* + c 4 B.

A: We have to find the indefinite integral of given function

Q: Consider the function f(x): - 4x + 6x - 8. f(x) has a critical point at x A. Find the value of A: A…

A: For critical points ofa function we first find the derivative of the function and equate it to zero.

Q: Explain why the Comparison test is not a good choice for showing that the following series…

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Q: Sketch a single graph of a function f which satisfies all of the following sign charts for f, f',…

A: We need to draw graph.

Q: Investigate the convergence of the following series. H.' 2n+5n 2) ΣΗ-1 ILJ! 3n

A: Here, the given series is: ∑n=1∞2n+5n3n Let, an=2n+5n3n; n≥1

Q: Find the Laplace Transform of the following functions: a. L(sinxcosxe*} b. L{

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Q: Find the vector 2u +3w given the vectors u =-i-4j and w = -2i + 5j. Write your answer in the form a…

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Q: Find the average value of f(x)= 4x - 5 from 1 to 3. ... The average value of f(x) = 4x - 5 from 1 to…

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: 24) Find the maximum rate of change of at the given point and the direction in which it occurs.

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Q: (6x- y+3)dx+(3y'-x-2)dy 6) Integration Factor Method rahee

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Q: -(1/3), 3/9, -5/27, 7/81

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Q: Change the order of integration. f(x, y) dy dx Jo

A: 0≤x≤10≤y≤xRegion bounded by:x=0, x=1y=0, y=x

Q: Find V. (V × F), if F(x, y, z) = 5e"*i+ 6xe®j– 2ek. V · (V × F)

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Q: As you will show, exponential growth functions ekx always dominate power functions x", and power…

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Q: y x = y - 2 y = 1 x = e -3 -1 1 2 4 | y = -1 3. 3.

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Q: Find the limits of integration ly, uy, Ix, ux, Iz, uz (some of which will involve variables a, y, z)…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find V· (F × G), if F(x, y, z) = 8xi+j+8yk and G(x, y, z) = xi+ yj – zk. V · (F × G)

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Q: Find the domain, x-intercept, and vertical asymptote of the logarithmic function and sketch its…

A: We have to find out

Q: sion into quadratic form, ax² + bx + c = 0, and ide %3D

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Q: Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x2 b.…

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Q: 2-2 +2)Xx+1) (*+1P Option 1 Option 2 1. (x +1) *+2 (x +1) Option 3 Option 4

A: This question is related to partial fraction decomposition, we will solve it using given…

Q: पेरडा test conerg ence and divergence

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Q: Evaluate the integral: (5si + 9s²j + 10k) ds Answer : i+ j+ k

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Q: 3. Use the Fundamental Theorem of Calculus to evaluate the definite integral 16 x Vx dx 4

A: Given: ∫416xxdx Simplifing the given integral∫416xxdx=∫416x(x12)dx                 =∫416x1+12dx…

Q: Find an arc length parametrization of r(t) = (e' sin t, e' cos t, le') r1(s) = (|

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Q: SHOW THAT THE DIFFERENTIAL EQUATION IS LINEAR EQUATION OF ORDER ONE 1. (3xy + 3y – 4)dx + (x + 1)…

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Q: What is the result of multiplication of complex numbers -V3+i and (cos +i sin )?

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Q: Verify Green's Theorem by evaluating both integrals ам y? dx + x2 dy dA ay for the given path. C:…

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Q: 3 + In?x dx

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Q: A swimming pool is circular with a diameter of 40 feet. Depth is constant along east-west lines and…

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Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

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Q: Evaluate the function at the given value of x. Round your result to three decimal places. Function…

A: Solve the given

Q: An arithmetic sequence is given below. 10, 3, -4, -11, th term d, Write an explicit formula for the…

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Q: Find the exact value of: 1 + cot (Write your answer in the simplest form, use fractions whenever…

A: Trigonometric values cot2π6=32=3 sec2π4=22=2

Q: 30. The temperature at a point (x, y, z) is given by T(x, y, z) = 200e¬x²-3y²-9;? where T is…

A: Rate

Q: [2.xyy' – y² +, Vy* +x* ; 4– %3D

A: ∫x2+a2 dx = xx2+a22+a22lnx+x2+a2+C

Q: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

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Q: x2 dx (x+2)3 In |x + 2| + 4x+6 (*+2)a +C In |x + 2| – 4x+6 (x+2)a

A: To integrate.

Q: Find the Inverse Laplace Transform of the following functions: 16 a. L4. s(s2-14) b. L4. (25-32)2

A: we have to find       L-1{16s(s2-14)}   we can re-write the function 16s(s2-14) =1614( -1s +ss2-14 )…

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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Q: 6. Find the indefinite integral. S 3x³ V3x4 + 7 dx (Use substitution method)

A: Solving the problem by finding the value of integration.

Q: Evaluate the double integral. 3r(1+ y²)¯ dA; R is the region in the first quadrant enclosed by y =…

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Q: Find the derivatives of the following functions: Inx i) y = sin3x? ii) y = e2*cosx iii) y = 3r+5

A: i)y= sin 3x2y' =ddx sin 3x2y' =cos 3x2  ddx(3x2)y'=cos 3x2 (3)(2x2-1)y'=(6x) cos 3x2

Q: Find the derivative of this function

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Q: d d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: 2. Compute Ja F · ds for F c(t) = (t , In(1+ t²), e*) for 0 <t < 1 VV, where V(r, y, z) = 4x² In(1+…

A: Find your answer below

Q: Prove that n2 +1 > 2? when n is a positive integer with 1<n<4.

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Q: Which of the following is undefined? cot() 131 A B sec(630") tan(-14n) D csc(-810")

A: Find which of the following is undefined.