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Advanced MathQ&A Libraryl Verizon ?10:53 PM87%Done3 of 3Instructor-created questionFor y = 5-x, Osxs2 sketch the graph of the function, and then for the region below y = 5-xa) Sketch 4 circumscribed rectangles and find (Sa) overestimateb) Sketch 4 inscribed rectangles and find (S,) underestimatec) For positive integer "n" find (Sn) overestd) For positive integer "n" find (Sn) undereste) Find the area of the region by finding the limit: lim(S,) where S, is from part (c) or (d)|(5-x²) dxf) Check your answer by evaulating)+f( 1 )+f()+f( 2 )] =unitsAx =2: S4) underestimate = Ax[f(5c) For positive integer "n" find (Sn) overestAx =; For (S)overest k =a+ (k -1)Ax = 0+ (k - 1)- (in terms of k and n)2 2JAx in terms of k and n)S,Σ) ΔΣ15-(Κ- 1ink= 1пS, = x)Ax = 10 +( -34 n(n - 1)(2n - 1)4.=10-2-n°k=1d) For positive integer "n" find (Sn) underest2Ax =; For (S)underest => C = a+kAx= 0 + k-: (in terms of k and n)s,- Σ ) Δκ Σ15-κJAx; (in terms of k and n)k= 1k=1n(n + 1)(2n + 1)S = Y flcAy = 10 +10-Question is complete.All parts showing!!Question

Asked Mar 26, 2020

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Step 1

Hi! We are answering for the red circulated part of the question.

**Note:**

For over estimation (upper Riemann sum),

where, f(c_{k}) = sup f([c_{k-1}, c_{k}]).

Step 2

Let us draw the graph for better understanding.

Notice that the function is a strictly decreasing function in the interval [0,2].

So, the supremum of the function will exists at ck-1 in the interval [ck-1, ck].

And

...

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