10. Suppose f and g are continuous functions and [ f(x)dx=7, [f(x)dx=2, and [g(x)dx =12, determine each of the following: -| f{x)dx b. [ f(x)dx [25(x)+3g(x)dx a. C.

Q: Suppose that f(x) is a function, whose derivative is f '(x)=(1 + cos x)(e* – 1)(x – 2)²(x – 3). At…

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Q: Suppose f is continuous everywhere, and | f(x) dx = -1 and 3 Find f(2)dz. f(x) dx 2. Find dx. Cannot…

A: As per our guidelines we are supposed to solve only one question i.e. the first question. For the…

Q: Suppose f(x) is the function such that for a > 0 we have f(x) = (e" – 1) In(x) and for x < 0 we have…

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Q: If fx) is a continuous function on [4,7] and F(x) is an anti-derivative of f(x) such that F(4)=9 and…

A: Given f(x) is continuous on [4, 7] and F(x) is the anti-derivative of f(x)                 F (4) = 9…

Q: 36 If f is continuous and f(x) dx = 6, find xf(x²) dx.

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Q: 00 Suppose 0 < f(x)< g(x) and both are continuous on [a, o0). If | 9(x) dæ diverges, 00 | f(x) dx.…

A: We have to apply the comparison test

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

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Q: 16 8 If f is continuous and f(x) dx = 10, find f(2x) dx.

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Q: 17. Suppose the radius r, height h, and volume V of a cylinder are functions of time t, and further…

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Q: 9. 6) Suppose that g is continuous and that g(x) dx = 2 and g(x) dx = 16. Find g(x) dx.

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Q: 15. If g(x) and h(x) are both antiderivatives of some func- tion f(x), then what can you say about…

A: Consider that gx and hx are both antiderivative of function fx. Find gx-hx.   Since gx and hx are…

Q: If f(x) is an even, continuous function for which = 4 and dx = 4, then f (x) dx 3 2

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Q: 2 If f is continuous and f(x) dx = 14, find | xf(x?) dx.

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Q: (a) It is possible to have E(XY)=E(X)E(Y) when X and Y are not independent.

A: We know that if the Karl Pearson correlation theory, If X &amp; Y are independent then we say that…

Q: b) Suppose x # 2. Find dif dx In y = In (x - 2)² √x² +1

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Q: We have found the following Wronskians. W = -e-³x; W₁ =-e-2x(4+ex)-¹; W₂ = e¯x(4+ e*)-¹ We want to…

A:

Q: 6. Determine the value of the constant a for which the function g(x) is continuous at x = 1 x2 + 5x…

A: This is a limit and continuity problem

Q: 4 Suppose that f(1) = 9, f(4) = -7, f'(1) = 6, f'(4) = -1, and f" is continuous. Find the value of…

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Q: If 0 < f(x) < g(x) for all x and I f(x)dx diverges, then | g(x)dx diverges. 13 Select one: True…

A: Given the statement

Q: 4.1 Suppose that fig and g'are continuous on the interval 1= {x :asxs b). Show that a ) exists, and…

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Q: 36 6. If f is continuous and f(x) dx = 2, find xf(x²) dx. %3D

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Q: Suppose that f (x) has a continuous second derivative f"(x), f(2) = 4, f'(2) = –1, and / f(x) dx =…

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Q: -2 x< -1 Q1)a) For what values of a and b is g(x) = ах — b -1<x<1, x21 Continuous at x= -1

A: The suitable formula for continious       LEFT HAND LIMIT = RIGHT HAND LIMIT

Q: If f:R→R is a continuous even function, then | F(x)dx is necessarily equal to -5 O10 O Cannot be…

A: A function is even if f(-x)=f(x)

Q: Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x ≥ 0…

A:

Q: Suppose that g and h are continuous functions and that S8(x) dx = 5, h(x)dx =-1, and h(x) dx = 3.…

A: There is no such rule of division of two integral.

Q: - if f(x) is a continuous function at x O, then a = 1-cos4x よく0 x? { a If f(x) = r= 0 r>0 V16+ VF -

A: Then to find the value of a if f(x) is continuous at x=0   Since for any continuous function at…

Q: '12 9. If f is continuous and f(x) dx = 20, find f(2x) dx.

A:

Q: x2 – 1, if x 1 Let f(x) (a) Is y = f(x) continuous at x = 1? (b) Is y = f(x) continuous at x = 2?

A:

Q: 2: The necessary condition for existence of the solution of the nonlinear equation x =g (x) in…

A: For any non linear function, to find the existence of its solution between an interval there should…

Q: 18 9. If f is continuous and f(x) dx = 14, find f(2x) dx. !!

A: Solution is in step 2

Q: If g(x) = - - S^*[e'- In(2t+1)]dt, find g'(x) . dx A ex-In(2x+1) 4 B

A: We can solve this as follows:

Q: 1. Where are the following functions continuous? x F(x) = ex + 4-x3 G(x) = 3x5 - 4x? H(x) = x-5x3…

A:

Q: 11. Suppose f(x) dr = 4, f(x) dx = 5, and | f(x) dx = –1. Then f(x) dx =

A: From given data: ∫03fxdx=4 .....1∫23fxdx=-1 .....2 From (1) and (2): f3-f0=4  .......3f3-f2=-1…

Q: Please see picture

A: Introduction:Here, MX (t) denotes the moment generating function (mgf) of the random variable X;…

Q: 4 Suppose that f is continuous function such that |F( x) # x and 4 [(4x)dx = 3. Then fxf(4x² )dx =?…

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Q: 1.5 If y is a continuous variable over (-0, 00) and f(y) = e¬*-e* intervals, then g(y) = S f(y)dy is…

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Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b - 1<x< 1, 3 x21 Continuous at x=1

A: From  the given problem:   gx=-2x≤-1ax-b-1≤x&lt;13x≥1     As we know that a function f(x) is…

Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b -1<x<1, 3 x21 Continuous at x=0

A: F is continuous at any point then left hand limit is equal to right hand limit. if limit is not…

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

A:

Q: 9 3 Iff is continuous and f(x) dx 8, find f(x2)dx

A: Given as

Q: 4. `s.] Find the number a and b at which f is continuous everywhere? x² -1 if x 2

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Q: 7. Suppose that the function f (x)=2-sin(e*) is continuous on with equal step 2'2 size, h equal to .…

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Q: a) Find the values of α and β such that the function f(x) = ( α cos x + 2 if x < 0 βe3x + αx2 if x…

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Q: h(x) = (5x-1 d) m(x) = (4x² – 9x} %3D

A: Product rule of differentiation: u·v' = u·v' + v·u'   ddxxn = n·xn-1 ddxf(x)n = n·f(x)n-1·f'(x)

Q: .3 Suppose that f is a continuous function and that f(x) dx = 6. Find f(3x)dx.

A:

Q: Suppose that h is continuous and h (x) dx = 12. Solve for 2 4 h(v20–4x -dx. Hint: note that h (x) dx…

A: Given that ∫24hx dx=12. Put u=20-4x. Then, du=1220-4x12-1-4 dx On simplifying, du=-220-4x dx

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.