Solve the differential equation Integrating Factor by Linear Equation: y' + X. (4)» = * y = x+

Q: The sum of one number and five times the second number is 50. A. What are the numbers so that their…

A: Let the first number be 'x' second number be 'y'. A/q  x+5y=50⇒5y=50-x⇒y=50-x5 The product of first…

Q: A function f has the following graph: 4- -3 -2 1- -2 -1 5. 6. 8. -1- -2- Which of the following is…

A: Graph of the function is given, we have to discuss about continuous of the function

Q: Find the area bounded by the curve r= 2+cos θ

A: Given problem:- Find the area bounded by the curve r= 2+cos θ

Q: 6. lim (sinx)* X0+

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Q: Determine whether the series converges or diverges. Make sure to clearly state the test that you're…

A: Given,  ∑n=0∞2xnn!

Q: Q1: Find the length of a and b in the following triangle a 75 30

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Q: A plane region is bounded by the curves 2x2 + 4x + y = 0 and 2x – y = 0. Sketch the given boundaries…

A: The objective of the question is evaluate the area bounded by the given curves and Sketch of the…

Q: Find V x (V x F) if F(x, y, z) = 9xyj+ 5xyz k. V × (V × F) :

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Q: Find the exact length of the curve. y (y-3), 4sys 16 X =

A: use derivative for finding the exact length.

Q: 6. lim (sinx)*

A: u =eln u, then:limx→0+  (sin x)x  =limx→0+  ex ln(sinx)=limx→0+  eln(sinx)1x=elimx→0+  ln sin(x)1x

Q: 6. Evaluate - x4 dx by making a substitution and interpreting the resulting integral in terms of an…

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Q: 5. Find the integral | 2(x* - x°) (x5 – 1)®dx x In(x + 2) dx а. d. | In x? dx | 2xe** dx b. е. 1 2x…

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Q: What theorem is used to solve for centroid? Pappus O varignon's O Castiglliano's O Pascal's

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Q: Q4: Find the corresponding Spherical polar coordinates of the Cartesian coordinates (6,2,5).

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Q: Find an equation of the largest sphere contained in the cube determined by the planes a 1, a = 7, y…

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Q: Find the critical points of the parametric equations x = 5 – Int y = t+ Int

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Q: Find V · (V × F), if F(x, y, z) = 2e"²i+ 2xe"j – 9ev²k. V· (V × F) =

A: Given F(x,y,z)=2exzi→+2xeyj→-9eyzk→ To find, ∇.(∇×F)

Q: fu)=Sin(x) aニT R=?

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Q: Repeated Imaginary Roots of Auxiliary Equations Solve the equations: 4) (D3 + 36D)²y = 0 5) (D3 +…

A: The given differential equation,4. D3+36D2y=05. D3+1002y=0

Q: Set up (but do not evaluate) an iterated triple integral for the volume of the solid enclosed…

A: A detailed solution is given below

Q: Evaluate the integral of (3x2 + 9y2) dx dy if the interior limits has an upper limit of y and a…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A: greens theorem

Q: I. INDETERMINATE FORMS: Evaluate the limit by employing Theorem 23. f(x) f'(x) lim = lim Equation 1…

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Q: Use the formula «(t) ||r'(t) × r"(t)|| to find «(t). r(t) = e12i + e-j K(t) = %3D

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Q: Find the particular solution of the DE y''-11y'+24y=0 when y(0)=2 y'(0)=-3

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Q: Find the area of the region bounded by  y=x^3,y=x+6 and       2y+2=0.

A: This is a problem related to integration. Based on the general formula and concepts we will answer…

Q: Find div F and curl F if F (x, y, z) = 10e*V i – cos yj+ 3 sin zk. %3D div F= curl F=

A: div F=∂Fx∂x+∂Fy∂y+∂Fz∂z∂Fx∂x =ddx(10exy)=10y exy∂Fy∂y =ddy(-cos y)=sin y∂Fz∂z=ddz(3 sin2z)=3(2sinz…

Q: Find T(t) and N(t) at the given point. r(t) = (t – 5)i + tj; t= 5 T(5) N(5) =

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Q: Find V. (V × F) if F(x, y, z) = 10 sin ci + 9 cos(2.x – 3y)j + 9zk. V·(V × F) =

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Q: M-2-Sin(X y) nd dm dt X = t. yclint Z=et-1

A: Differentiation

Q: Using the shell method, determine the integral that represents the volume of the solid formed by…

A: volume rotating about x=pii

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where o sts 1. (y – x) dx +…

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Q: Find r'(t), r"(t), r(t)•r"(t), and r'(t) × r'"(t). r(t)-흑러 - 26 + (a) r'(t) (b) r"(t) (c) r'(t) ·…

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Q: | (csc 0)(1+ sin? 0 + sin 0 cot? 0) do а.

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 3…

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Q: For the given vectors a and b, find the cross product a x b. =(3,0, -1), b = (3, 2, 0) a %3D a x b =

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Q: 3.) ž sin'(x)dx

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Q: pe of a trail at a distance of x miles from efinite integral of f(x) from x=3 to x=5

A: answer is in next step

Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 9x from (9, 9) to (0,0). NOTE: Enter…

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Q: Find V × (V × F) if F(x, y, z) = 9xyj+10xyz k. V x (V × F) =|

A: We have to find given expression.

Q: dy For each of the following functions determine dr

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Q: Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: -x lim + 169 x→-9 x+9

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Q: The following telescoping series 00 1 Σ- en+1 – en+2 n=1 converges to Ve the above none of them…

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Q: dx 4. Find the integral 2-1)3 a. In (**1) b. In () - + C x-1 2x2-2 + C x-1. 2x2-2 c. - In -+ C 2x2-2…

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Q: Find curl (3z i + 4x j+ 7y k). curl (3z i+ 4x j+ 7y k) = ( i )i + ( i j+ ( )k

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Q: Use the formula r(t) - – P) x r"(0)|| to find giớ). ||P() × to find x(t). r(t) = e!l"i + e tj 156…

A: Given problem:- Find k(t) of r(t) =e12t i +e-t j

Q: Find the curvature and the radius of curvature at the stated point. Edit r(t) = 8 cos(t)i+ 7 sin(t)j…

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Q: Solve the problem. Let D be the region bounded below by the cone z-x2+y2 and above by the sphere z-…

A: Given