Which of the following limits is equal to a* da? 4 A lim T 00 k 3+ n k lim (3+ 2 T 00 n k-1 C lim T 00 2k 3+ 4 2 D lim T 00 k=1 2k 3+ n

Q: Q3: Solve the following first order differential equations Use any method: 1. e + 2x dx + e x dy = 0...

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Q: Q1: Find the solution of the following Differential Equations d²y 1. + y = 6e* + 6 cos(x) dx2 d?y 2....

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A: here point are (x,y,z) =(5,-3,-2)                        (a,b,c) = (-2/3 , 2/3 , 1) parametric equat...

Q: 5. Solve 5-X Express your solution in erval no solution on a real number line.

A: We we will solve the inequality. 

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A: Use inverse trigonometry function formula.

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A: Solution of the problem as follows

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Q: Prove the following: sin² 0 – cos² 0 = 1– 2cos² 0 %3D

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Q: 4 5 y = x? – 8x – 6 + - 8x – 6 +a

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Q: Separation of Variables: Solve for y' = yx' O x4 = y In c Ox = cy

A: To solve the given differential equation by separation of variables  

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A: If z is parallel to a vector u then u =lemda z 

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Q: 1. x3 + y3 – 2xy = 0, find y'.

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Q: III. Derive the following HCA 1. The unity rule: = 18 dx du dx 2. The quotient rule: xp dx

A: f(x)=xDerivative formula:f'(x)=limh→0 f(x+h)-f(x)hf'(x)=limh→0 (x+h)-(x)hf'(x)=limh→0 hhf'(x)=1ddxf(...

Q: Consider the points A(2, –3, 4), B(4, –5, 1), C'(-2, –4, 1), and D(4, 2, –6). (a) Find the volume of...

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Q: 2. Find the area between the curve x= - y +y + 2 and the y- axis.

A: 2) To find the area between the curve x=-y2+y+2 and the y-axis. The region bounded by the curve and ...

Q: 4. Determination of Integrating Factors: Solve the equation y (4x + y) dx – 2 (x² - y) dy = 0 O 2r? ...

A: Given

Q: Find the vector component of v = 2i –j+ 3k along b = 4i + 8j + 8k and the vector component of v orth...

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Q: Determine the homogeneity of the following function x^3-xy+y^3

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Q: Q3: Solve the following first order differential equations Use any method: 3. y cos(x)dx + 3sin(x)dy...

A: Since you have asked multiple questions in a single request we would be answering only the first que...

Q: Graph the function f(x) = x+4/x Graph the secant line that passes through the points (1,5) and (8,8....

A: To graph the function fx=x+4x.To graph the secant line that passes through the points 1, 5 and 8, 8....

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Q: -2 sin x where y () = 7 dx O y = 2 cos x + C O y = -2 cos x + C

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Q: its principal argument. 12. Suppose the complex number z is situated along the real x axis, then the...

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Q: 3. Solve this third-order ODE by using the method of undetermined co- efficients: y" – y = exp x . -...

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Q: Find the centroid of the region bounded by the curves: x + 2y = 6 = 0 y=0 O A = 3 sq. units; Centroi...

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Q: ner order ential e = 0; y(1) = 0, y'(1) =

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Q: 6. (Sections 8.8 and 8.9) Determine whether the following piecewise-defined function is a probabilit...

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Q: 3. Check if the following is a separable equation. dy dx O variable separable not variable separable

A: dydx=-xyRearrange the equation;y dy=- x dxf(y) dy = f(x) dxYes,the given equation is variable separa...

Q: Solve the differential equation. ху' — 2у %3D х2, х>0

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Q: 4. S 2z3 el-z dz 5. S Vx In(Vx) dx Vr3 6. Si, Inx dx

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Q: etermine if the series is convergent or divergent. Show your work, and clearly state the test used n...

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Q: b Let y = x²sin(y) + yeXy, where x = s + 2t and y = st dv when s (ii) dt = o and t =1 is [d]

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Q: Find the following: 1.) A +B = 2.) A x B =

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