the following theorem. Theorem If f is integrable on [a, b], then b [ºr(x) dx f(x) dx = lim f(x₁)AX n→∞ where Ax = i = 1 (x² b-a n and x; = a + iAx. iven theorem to evaluate the definite integral. 9 [₁²³ 4x + 9) dx

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A: Given :- Zeros of degree 3 polynomial are 6i and 45

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A: Please see the below picture for detailed solution.

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A: To find integral

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A: Given query is to find critical point and inflection points.

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A: Check the each options for the given field is conservative or not.

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A: y=(x+59)32 from x=0 to x=3arc length(L)=∫x1x21+(dydx)2dxd dx(xn)=nxn-1

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Q: 14. Evaluate the limit for the graph: lim f(x). x → 1 4 a. +∞o b. 1 T y4 4 2 20 +2 T 2 4 c. 3 d.…

A: see below the answer and explanation

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A: Given Table : X Y 1 884 2 1149 3 1618 4 2190 5 2962 6 3705 .

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

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Q: 6. Find the limit. Show your work algebraically. lim x48 (5 + 2/7)

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Q: If f(x) = ax³ + bx² + cx+d, where a, b, c, and d are constants, find f"(x). 6ax+ 2b 6x + 2 a+b+c+d…

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Q: Find lim 1 2x217 a. x→ 0* 5 (x-6)2/7 b. x→ 0 as C. X→ 6* d. x→ 6

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Q: they​ occur, for the function f(x)=x2−18lnxon the domain [1,11].   Select the correct choice below​…

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Q: Evaluate the limit for the graph: lim f(x). X+2+ O -4 +00 0-1 01 -00 4 2 -20 -2 24 4 8

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Q: 3. Identify the graph of f(x,y)=x²-x+3y² +12y-13, state where it attains its minimum value, and find…

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Q: Find all critical points of the following functions. રી. f(x)= x² + 10x + 43 -

A: according to bartleby guide line we do only first part (A)  f(x)=-x2+10x+43d dx(xn)=nxn-1

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Q: 5. Find the points of inflection and discuss the concavity of the function (x)=-8x-2 cos x on the…

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Q: 2. a) Estimate the instantaneous rate of change of the function at the tangent point (7,9) indicated…

A: Given,

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Q: Use l'Hôpital's Rule to find the limit. In (x²+7x) In x lim X→0* lim X→0* In (x² +7x) In x = (Type…

A: K=limx→0+lnx2+7xlnxd dx(xn)=nxn-1d dx(lnx)=1x

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Q: Complete the following steps in order to find a vector-valued function r(t) that satisfies the…

A: Please see the below picture for detailed solution.

Q: Is this fully simplifed ?

A: Find y' for the function y=6x-3x2+7x.