1. Determine the area of f (x) = 3 + 2x – x² and above the x axis. - X - 3x 3 3 2. Determine the length of y = between 0 < x<¬(3)2. 2 3

Q: 7. Find the area between f(x)=-x² + 4x and g(x) = x² - 6x +5 over the interval 0≤x≤1 Ei..

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Q: 3x What is f'(x) given the integral function f(x) = (4u – 2) du? O f'(x) = 4x-2 %3D O f'(x) = 12x -2…

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Q: Hello! What is the solution to this question? Thank you for your help! Have a nice day :)

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Q: #46

A: We need to find the value of b such that the function g(x) is continuous at every x,

Q: 3. Compute the value of F.dr if F = -yi + xj and C is a semicircle from (-1,1) to (1,-1).

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Q: If g(1) = -1, g(5) = 2, and | g(x) dx = -9, evaluate the integral %3D æg'(x) dx.

A: Given: g1=-1  and g(5)=2∫15g(x)=-9

Q: 1. The area between the graphs of f(r) = x² + x + 5 and g(1) = -r² – 21 + 14.

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Q: The integral of x²Inx with respect to x is; r3 A -(Inx – 3) +C 9 B -(3lnx – 1) + C 3 C ( 3lnx + 1)…

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Q: (f) p(xj,...X) =E

A: Degree is n.

Q: 1) Find the absolute extremum values of f(x) = x? [1, 2]. 2x +24 over the interval %3D -

A: Topic - maxima minima

Q: 3. Consider the function: f (x) = v16 – x² + 2 a. Sketch the graph. b. Using geometric formulas…

A: Given: (a) The above equation can be rewritten as follows, Squaring on both sides, The above…

Q: Use the result obtained in Problem 20 to find the areaenclosed by f(x) = - x2 + x + 4, the x-axis,…

A: Given, the area is enclosed by f(x)=-x2+x+4 the x-axis and the lines x=-1 and x=1

Q: +[ƒ Given that 5 ≤ f(x) ≤ 6 for -4 ≤ x ≤7, use property 8 of Section 5.2 of the Stewart Essential…

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Q: 1 1 The integral x²dxdy represents the 0, area under the curve y = x² between x = 0 and x = 1.…

A: Given integral is ∫01∫01x2dx dywe know that ∫ab∫cd f(x,y) dx dy represent areaonly when f(x,y)=1

Q: (a) Evaluate the integral ſ x e2x çdx (2x+1)²

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Q: Suppose that f(1) = 1, f(4) = 6, f (1) = 7, f '(4) = 5, and f " is continuous. Find the value of xf…

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Q: Find the integral. |(2x3 - 3x2 + x – 1) dx A x² + B 6x2 - 6x + 1 + C (c) None of the above x2 - x +…

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Q: For what value of b is

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Q: 8. Evaluate the integral S xydx from x=3 to x=6 when x = 6cos0 and y = 2cose A. 9/7 B. 9/3 C. 5/3 D.…

A: Topic:- integration by substituting

Q: Find the value of c which satisfies the conclusion of Rolle's Theorem with the given f (x) =x- 3x,…

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Q: 2) An elastic tire is described by the iven by the function f(x, y) = 4xy. Use

A: Introduction: The Lagrange methodology is employed to maximize or minimize a general performance…

Q: Evaluate the integral. 9 17 1+ x2 dx V1- x2 +C

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Q: A function f is approximated by a cubic spline defined by: 1+x+x² + x³ -{4+ 6(x-1) + 4(x- (4 + 6(x −…

A: Sol:- Consider the function between (0,1) ∫011+x+x2+x3dxApply the Sum Rule:…

Q: NUMMTD FE Evaluate the integral of f(x)= 400x* – 900x* +675x –200x² + 25x +0.2 between the limits…

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Q: 64. If f(r, 0) is a constant function and the area of the region S is twice that of the region R,…

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Q: 9 Evaluate the integral f 2x (x² + 1)° dx using the substitution = x² + 1. и — с 2.x (x? + 1)° dx +C

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Q: 1. Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

A: see 2nd step

Q: 4. Find the exact values of each of the integrals below. (a) / f(x) dæ f(x) dx f(x) dx dx -2 -2 (c)…

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Q: 11. Find two different antiderivatives of the function f(x) = 6x² +2ex. 1

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Q: 9-x2 18-x²-y² xydzdydx. B: Find the integral fo J

A: Triple integral

Q: If f(x)= the definitive integral from 3 to x of (t2+5)1/2dt, find f'(5).

A: Given : fx = ∫3xt2+5

Q: 7. Evaluate the integral r8-2x (x + y + 1)-2 dydr.

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Q: 7x Evaluate the definite integral : dx (6x2+2)2

A: Given,          ∫017x6x2+252dx

Q: 22 + 8x Use the Fundamental Theorem of Calculus to find the "area under curve" of y between x = 1…

A: It is given that, y=-x2+8x   between x=1 , x=5.We have to find the area under curve.

Q: nd the absolute extrema of the function defined by f (x,y) = x² – 2xy + 2y if the domain of is the…

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Q: 1. Use integration by parts to prove the reduction formula S(Inx)" dx = x(lnx)" – n S(Inx)"-1dx. %3D

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Q: (4) Recall the formulac: (5) Find the integrals: • ftan² (x) dx t: Is ta SC

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Q: F(x) V16 – t² dt 4-x3 ||

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Q: A function f is approximated by a cubic spline defined by : (1 + 2x -x³ (2-(x-1)-3(x-1)² + (x-1)³…

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Q: Sketch the graphs of the functions. (x) = Vx and g(x) - x² 10 10 -10 5. 10 -10 10 10 -1아 y 10 -10 10…

A: To find the area enclosed by the graphs fx=xgx=x2

Q: If f"(c) = 0, then f(x) cannot have a local extremum at x = c.

A: We know, if f"(c) is negative then f(x) have local maximum at x=c and if f"(c) is positive then f(x)…

Q: | For what value of a is Sx² – 1, x< 3 |2ax, f(x) = continuous at every x?

A: Let f is continuous at x = 3 then left and right limit are equal.

Q: 3. Let f)=x+x+2x-1E2,lx). Then x= 1 is a root for r() of mmltiplicity 3D1 None 4 2

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Q: 9) Given the function f(x)=-3x+2 , find the net signed x-axis over the interval [-5,3]. area between…

A: Given function is  f(x)=-3x+2 We have to find the area of the region bounded by the given function…

Q: 2 1. Use Simpson's rule to evaluate | dx , by taking n=4 o V1 + x* 2.Find the Area, enclosed by the…

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Q: 2. Find the principal part with respect to x for x 0 of the infinitesimal f(x) = = Vx + Vx. (That…

A: We have to use expansion of the function after some manipulations.

Q: Consider the region bounded above by g(x)=−9x−9 and below by f(x)=x2 −9x−18. Find the area, in…

A: Calculation:The given curves are f(x) = – 9 x – 9 and g(x) = x2 – 9x – 18.The area enclosed by two…

Q: Find a finite difference approximation of Cf(x) + Df'(x) using the points f(x – h), f(x), and f(x +…

A: Let f be any function defined on a vicinity of the fixed x , and let h &gt; 0 representing apositive…

Q: If f is a quadratic function such that f(0) = 9 and f(x) x2(x + 1)3 dx is a ratianal.functian,,find…

A: This question is about finding f'(x)  at x=0  where f(x) is a rational function

Q: Q3) For what values of a and b are -x² + a , x Continuous at every x ?

A: