Suppose is a real number constant. Evaluate the limits, writing your answer in terms of 3 where appropria write DNE. A. lim+1+ B. limx→0 Bcos(x) x²-x e te-2 Ba² 5224 C. limx→∞ 33-4x+2

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A: Please see the below picture for detailed solution.

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A: we know that   dxndx=nxn-1d(secx)dx=secxtanx

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A: We will find the required

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A: (4)   I=∫xsin(2x2)dx∫sinxdx=-cosx+cdxndx=nxn-1

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A: A matrix A is invertible if the determinant of A is not equal to zero.

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A: Given f(x) = x4−256x+4

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A: "Since you have posted multiple questions, we will provide the solution only to the first question…

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A: We need to solve D.E.

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A: Solution: dxdt=0.5x-0.002x2-0.001xydydt=0.6y-0.001y2-0.006xy

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A: The polar equation is  r=2 sin θ

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A: To find the interval. By the given graph.

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A: To find the solution.

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A: We know, L{y"}=s²L{y}-sy(0)-y'(0) L{y'}=sL{y}-y(0) L{eat}=1/(s-a)

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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A: We have  f(x)= 8x+8 and g(x)=8-x2

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A: 16) The given equation is; Sinx - Cosy - 2= 0

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A: Consider the function below and its graph shown below.ft=14t  if -10≤t&lt;0t22  if 0≤t≤10Let Fx=∫-5x…

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A: Solved below

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A: We can find the area of the region .

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A: To find the area of the shaded region.