Determine whether the series converges, and if so find its sum. 4k+2 Σ 7k-1 k=1 1) This series can be rewritten in which way? k+2 1 73 k=1 k-1 43 k=1 Σ 43 7 k=1 k-1 4 Σ k=1

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A: Limit   If a constant number is decided by infinity then it will tend to zero .

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Q: 8. The differential equation (2x' -xy² -2y+3dx-(x'y+ 2x)dy =0 is exact because ON

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A: We will find the degree of differential equation in the following step.

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A: Function change and slope     Answer is  192

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Q: Write the first five terms of the sequence: { +o0 11 In n n=1 Determine whether the sequence converg...

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Q: 7. lim 4?* 8. lim e 9. lim e 10. lim e*

A: To evaluate the given limits.

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A: To evaluate the given limit , substitute  x= -5  in the given expression.

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Q: If log, (8) z 0.7 and log, (7) z 0.6, find the approximation of log,(448) =

A: Follow the procedure given below.

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A: Given,y" - 7y' = (2x-1) sin2xNow substituting the value:y" = D2yy' = DyD2y - 7Dy = (2x-1) sin2xD2y -...

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Q: Find fla) for f) = x? +6 Aind fre) for fY) = x-5_ Frnd flay for f(x) = × ² -4x+} Find fr x) for floc...

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Q: Answer the question below: Let h(x, y, z) = ze*y + x² cos(z) cot(y³). The student should find hyzx.

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A: The given integral,                ∫-∞182x-32dx

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A: True, Differentiability implies continuity.

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A: Follow the procedure given below.

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A: We can find the integral as below using substitution method

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Q: 18. lim 19. lim 20. lim log, x

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Q: x'cos x dx cos x Jo

A: LetI=∫0πx3cosxdxUse integral by partsI=x3∫cos(x)dx-∫∫cosxdx.ddx(x3)dxI=x3sinx-∫ 3x2sinxdx0π         ...