Find the area (in square units) of the region under the graph of the function fon the interval [-1, 3]. f(x) = 2x + 8

Q: The function f(x) = 3x³ + cos(3ræ) + 2x , x > 1 is known to be a strictly increasing function on its…

A: Given f(x) = 3x3 + cos(3πx) + 2x,  x≥1   ⇒ f'(x) = 9x2 - 3πsin(3πx) + 2

Q: df Use integration to find f(4) if- dx O 42.667 O 43.667 O 47.667 O 48.667 = 2x² and f(0) = 5.

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Q: 3 Let f(x) = 2 + In(bx), where b is a positive constant. Find f'(x).

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Q: The range of F in F(x) = 2 sin x; - < x< 2 T is: %3D -2SF(x)SO F(x)S2 ) -2SF(x)S2 O O

A: Given:- F(x)=2 sinx  ,-π/2 &lt;x &lt;2π To find:- Range of F(x)

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: 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: Find the critical numbers of the function f(z) = 2x'-24r. Answer (separate by commas): I = Il

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Q: Find the absolution extrema of f(x) = (In x)2 on [1, e].

A: We have to determine absolute extrema of girls question

Q: Find the residue of the function f(z) = 1- e2z at its pole. z4 |

A: The given problem is to find the residue of given complex variable function at its pole, we can use…

Q: Suppose f is a continuous positive decreasing function for x ≥ 1 and an = f(n). By drawing a…

A: To determine  Remainder Estimate for the Integral Test

Q: Find the average of the function g (x) = 2 cos 2x on the interval [0, r] -T

A: The function f(x)=2 cos 2x on the interval 0,π

Q: The area of the region in the xy-plane enclosed by the x-axis, the curve y = f(x), f(x) 2 0, and the…

A: given: a function y=f(x), f(x)≥0. the area of the region in the xy plane enclosed by the curve…

Q: The function f(x)= (x² – 1)³, is decreasing on the interval (- 00 , – 2) U (0,2) ^O (-1,0)U (1, ∞o )…

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Q: 1) Find the absolute extremum values of f(x) = x² [1, 2]. – 2x + 12 over the interval

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Q: et f(x) = x3- 3x2-1,  x ≥ 2. Find the value of df-1/dx at the point x = -1.

A: Let f(x) = x3- 3x2-1,  x ≥ 2. Find the value of df-1/dx at the point x = -1.

Q: A graph of f(x) = -2x + 4 is shown above. Using the geometry of the graph, evaluate the definite…

A: We have to evaluate the given integral by using the geometry of graph .

Q: Q2/ Find the dirivative for the follwing function y = cosh(x)/ln(x)

A: Given: To Find:

Q: Calculate the approximation for the given function and interval. M5, f (x) = ln x, [1, 3]

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Q: The function f(x) = x2 – 8x + 12 is positive on (0, 2) and (6, 10) and negative on (2, 6). Find the…

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Q: Find the average of the given function on the given interval. (a) y = cos x, [0, 3π/2] (b) y = x² +…

A: a) y=cos x, 0, 3π2b) y=x2+x+1, 0,1

Q: (a) Find the linearization L(x) of f (x) = v25 – x² at a = 3. (b) Use the linear approximation L(x)…

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Q: 2) Consider the function g(x) = x³ + 3x? – 9x + 2 on the interval [-4, 2]. Find all local extrema,…

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Q: 2. Given the graph of the function f(x) below, use a midpoint approximation with 4 rectangles to…

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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: 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: Write the rational function as a sum of partial fractions: x+1 A B -- A = J.B = + (x-4)(x+7)¯ x-4…

A: Given that, x+1x-4x+7=Ax-4+Bx+7  ----(1) To find A and B, Taking least common divisor on the right…

Q: The absolute maximum of f(x) =x² – 4x on [0,3] is y= OA. OB. 4- o 3- OC. OD. 0.

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Q: Find numbers a and b, and c, so that f is continuous and differentiable at every point. 4) x- + C,,…

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Q: Find the absolute maxima and minima of the function on the given domain. f(x_ v) = 2x + 5y on the…

A: Given function f(x,y)=2x+5ywe need to find criical pointconsider f'(x)=0                     and…

Q: - The antiderivative of f (x) =; whose graph passes through the point (C 3+5sinx+. +3cosx 1(. 5 1(.…

A: Introduction :

Q: Use the midpoint rule with n=5n=5 to estimate the value of the integral:…

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Q: Calculate the rectangular approximations R1, R2, and R4 for f(x)=2x−1 over the interval [1,5].

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Q: Find the average vale ot f(x)=Dx²e-2x overthe interval [-1,1]

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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: 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: d. Find the linear approximation L(x) for f(x)=x²-x-1 at a = 1.

A: Given function is fx=x3−x−1. d We have to find the linear approximation Lx for function fx at a=1.…

Q: 2. Use partial differentiation to approximate the following sum, not the individual radical. V81 +…

A: According to question,Given expression,81 + 263

Q: Find the absolute extrema of the function f(x,y) = xy - x - 3y on the triangular region with…

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Q: 2 If f is continuous on [0, 2] and f(x) dx = 5, find the value of | f(æ – 2) dæ.

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Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of at x = 1. %3D df-1 - dx

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Q: 24.) Given the function f(x)=x²– 2x Estimate J f(x) dx using four subintervals by . finding R4, L4…

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Q: Consider the following equations. f(x) = Vx + 2 g(x) = * + 2 Sketch the region bounded by the graphs…

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Q: Find the linear approximation L(x) of the function f(x) = (1-x)1/2 at a=0 and then use L(x) to…

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Q: 11) Find a function y-f (x) that satisfies both conditions: d - 6x -4x+5,f(-1) =3 dx %3D dy 2 3 ==+…

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Q: Find the number b such that the average value of f(x)=2+6r– 3x on the interval [0.b] is equal to 3.…

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Q: 2. Use the secant method to estimate the root of f(x) = a° + a³ + 3. %3D By starting with the…

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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: 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: 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

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.