The Intermediate Value Theorem guarantees the existence of at least one real zero of the polynomial function g(x)= x³ + 1 on all the following intervals except: O [0,3] O [0,2] O [-1,2] O [-1.0] Search 9:15 PM 4/19/2023 [ ●

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A: (a) To find the surface area of the part of the plane that lies inside the cylinder, we first need…

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A: r=1+cosθr=3cosθ

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A: given y=elnxformula used→(i) d dx(xn)=nxn-1(ii)  we know→ elna=a

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A: a) pass through point 0,0slope =  tanπ6 = 3b) pass through point 3,3slope = infinie (vertical line)

Q: g(x)=√1 + 2x

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A: Where we have integral, need to perform double differentiation.

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A: a.

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Q: 5. Use variation of parameters to solve. y" - 2y' + y = 1+x²

A: **As per our guidelines, we are supposed to answer only one question at a time. Since you have…

Q: Find the indefinite integral for the function (2y — 9)-5 dy = - (2y - 9)-5dy AY

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A: Here we have a function g(x) need to find the average rate of change and equation of the secant.

Q: 1. Derive the expansion sin(2²) 11 -1% 22 1 22 3! + 5! 10 7! +... (0<=<∞0).

A: We shall use the expansion of sinx

Q: 2. Prove that the difference of an odd integer and an even integer is odd.

A: Prove that the difference of an odd integer and an even integer is odd

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Q: Determine the equations of any asymptotes for the following functions. x²-x-6 rẻ -5x+6 f(x)=

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Q: Evaluate f -dx 3 x²+3x¹ x² 1

A: Integral

Q: - Determine the given indefinite integral f(2x+1)x²x²+2x dx

A: let  B=∫(2x+1)e2x2+2xdxB=∫(2x+1)e2(x2+x)dxwe know→(i)  d dx(xn)=nxn-1(ii)  ∫eaxdx=eaxa+c

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A: Given data for the question is÷

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A: d(u.v)/dx = u.d(v)/dx + v.d(u)/dx

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A: given  S(t)=700e0.07twhere t is the number of years

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A: Note:- Since you asked multiple questions ,according to our policy we can solve only first question…

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Q: 13. f(x, y)=x²-2y³ - 5x+6y-5

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Q: Consider the following function. f(x) = 8x² - 4x Find the limit. lim Az-0 f (x + Ax)-f(x) Ax

A: fx=8x2-4xTo find : Find the limit                   lim△x→0fx+△x-fx△x

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