At what interval is y=3x5-5x3 decreasing O x>1 O -1

Q: Find the value of the constant C for which the integral 3 3C dx x + 25 X + 5 converges. C =

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Q: Find the critical numbers of the function. f(x) = x² log,(x? + 2)

A: fx=x2log7x2+2⇒fx=x2logx2+2ln7      ∵logab=logblna Critical numbers are the values of x for which…

Q: Sketch an approximate graph of g onthe interval0<=x<=4 g(x)=\int_{0 }^{x}( f(t)) d t Identify…

A: Let F be the anti-derivative of the function f. Calculate the indefinite integral of ft with respect…

Q: Starting from the function f(x) = e¬alx| -L 1 where

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Q: The value of the definite integral' f(x )dx for f(x) = 3 is:

A: We are going to evaluate the value of the given definite integral for f(x)=3

Q: 5x The interval over which the function f(x)= e (1+x) becomes continuous is O [-1, 0) O (-0,…

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Q: O Find absolute extrema for f(x)= x*-6x² +9x +l in terval [0,5] Gn

A: Given that fx=x3-6x2+9x+1To find : absolute extrema on interval  0,5Solution…

Q: Let L(x) = ln(x² + 4x + 14) in the interval [-10,10]. What are the absolute extrema of L(x) in this…

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Q: Consider the function f(x)=−2x2 +2x−3. Find the critical point, A, of the function A=? At x=A,…

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Q: Given the function h (x) = : x+1 Over what interval(s) is h (x) decreasing?

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Q: 10. f (x) = x² + 4x + 4 Opens up/down:. Vertex: Axis of symmetry: Solution(s): y-int: Domain: Range:

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Q: 25 If f is continuous and f(x) dx = 8, find xf(x²) dx.

A: given ∫025f(x)dx=8∫05xf(x2)dx=?

Q: Find values at x where the fuction is NOT differentiable(in any) f(x)= lx-2l +3

A: Given function is By definition, we have Therefore,

Q: Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ≈ T₁(x) when x lies in…

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Q: Find the linear approximation of f(x) = ln x at 1 and use it to estimate ln(1.33). L(x) In(1.33) =

A: Given : fx = lnx

Q: Find the value(s) of k that makes the function continuous over the given interval. 0 sx s2 2 < x s…

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Q: Ql.a- for what value of (k) is the function y= f(x) continuous at x=2 V7x + 2- V6x +4 -2 sx and x #…

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Q: 2. Find the interval [a, b] for which the value of the integral (2 + x − x²) dx is a maximum.

A: ∫ab(2 + x -x2 )dx here for get maximum value we have to differentiate the function  so here first…

Q: The function f(x) = x + 1/x is O Decreasing on (0,1) O Increasing on (0,1) O Increasing on (-1, 0) O…

A: Answer is written below

Q: The value of k that makes x2 – kx + 2x – 2k f(x) x # -2 x + 2 4, continuous at x = -2 is x = -2 O 2…

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Q: Given f(x) = (2x – 3)' (x +1). Determine (if any) (i) Critical point(s) for f(x), (ii) The interval…

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Q: 7. For what value of the constants A and B is the function f continuous on (-0o, 0)E AV-x+6-1 for x…

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Q: Given function: f(x) = critical point x is =_ 9x2 – 4x + 9, then the %3D O 0.89 O 2.25 O 0.44 O 0.22…

A: We have to check

Q: If f(x) continuous for x 2 0, and F(s) is defined by F(s) = | f(x) e *dx, where s > 0 Find F(s) for…

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Q: S/ kx +1 O<x<1 a) Let f(x)= %3D 2x+3 13x<3 Find the value of k, given that the function f is…

A: If the function is continuous at some point , then the value of both side of function is equal .

Q: Find the x-value corresponding to the absolute minimum value of f on the given interval. (If an…

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Q: What is the critical number c and function value f(c) of f(x) = (x – 2)² + 3x – 3. If necessary,…

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Q: Find f'( – 2) for f(x) = ln( (x* + 3)´) as an exact fraction or rounded to at least 2 decimal…

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Q: Consider : f(x)=e 2 , f'(x) =-xe 2 f"(x) = x'e ? Find for f(x): a) The critical number(s). b) The…

A: Consider   fx=e-x22 f'x=xe-x22  f''x=x2e-x22-e-x22 Find   for  fx a The critical Number sSolution:-…

Q: The average rate of change of Ax) = x +x -x-1 over the interval o<xs1 is -2 1 O -1 2

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Q: Find the absolute extrema of the function on the closed interval.

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Q: Q1: From the given graph of f(x) = sin x; [0 ,27] , f ind: (a)The critical points. 211 -2…

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Q: 5. At x=0, which of the following is true of the function* n y = x? + e2 O A. f(x) is decrea sin g O…

A: if f' of a function &gt; 0 then f is increasing if f' of a function &lt; 0 then f is decreasing.

Q: Ok(x) = Vx – 8 |- O f(x) = x Og(z) = |æ| + 5 Og(x) = x + 4, x > 0 1 Of(x) = Ofle) -

A: We have to choose the correct answer from the given option

Q: The function f(x) = x + 1/x is 2p O Decreasing on (0,1) O Increasing on (0,1) O Increasing on (-1,…

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Q: For what value of the constant a is the function continuous on (-0, 0). for r 1 f(x) ax a =

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Q: For a. y′ =ln(y)+x,withy(1)=1. (Here x0 =1.) b. y′ =ln(1+y),withy(1)=0. (Here x0 =1.) Is it…

A: Solving for  a) y'=ln(y)+x            dydx=ln(y)+xdy=ln(y) dx+x dx Integrating:           ∫dy=∫ln(y)…

Q: The absolute maximum of y =-x + 2x +3 on the interval [0, 3] occurs at Select one: O a. None of…

A: Simply take the derivative and equate to zero than solve for x.

Q: Find a nonzero value for the constant k that makes the function (tan(kx) x < 0 f(x) = Зх + 2k?, x 2…

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Q: Where does f(x)=- have a critical point, which is not an extremum? O O O x = -1 x=0 x = √√3 x = 1 x³…

A: From the above function , we get 3 critical points at X=0, -√3 and √3 and two point where function…

Q: se N.P.M. to estimate the root of -X = e -X for an initial of Xo =0

A: Here f(x)=e-x-x,  x0=0. We estimate the root of f(x)=0 by using N.R.M.

Q: Sx". .n-1 + n[x²- x" sin x dx = -x cos x + n cos x dx

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Q: Consider the function f(x) = x - 3 ln(x) on the interval The absolute maximum value is and this…

A: Consider the given function, fx=x-3lnx differentiate the function with respect to x,…

Q: b. False. The interval of integration [-1, 1] contains 0 at which function and the above theorem…

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Q: Find the lengths of the functions of x over the given interval. Approximate if necessary. y=e^x on…

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Q: (1) Locate the absolute extrema of the function on the closed interval. (a) y=4 sin x, [0,2n] (b)…

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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: Where does x3 f(x)= х2 —1 have a critical point, which is not an extremum? O At x=-V3 O At x=-1 O At…

A: Second derivative test :  when a function slope is zero at 'x' , then the second derivative at 'x'…

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 the general solution using Reduction of Order: x2y''-xy'+y=0 y1=ln x

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