Use the Fundamental Theorem of Calculus to cvaluate (1 - da

Q: Find the indefinite integral. Hint: Let u = 5- Vx. (Remember the constant of integration. Remember…

A: To evaluate the given intgral.

Q: Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of…

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Q: Suppose that 4 J of work is needed to stretch a spring from its natural length of 24 cm to a length…

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Q: If y = a + b/x , then the linear form of the following equation is

A: We can solve this as follows:

Q: Estimate the area under the graph of f(x) 1 over the interval [3, 7] using five I+ 2 approximating…

A: The given function is f(x)=1x+2 over the interval [3, 7] We have to use five approximating…

Q: 5) Find the value of the infinite geometric series. a) 500 - 100 + 20- 4+...

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Q: Find the area of the parallelogram that has two adjacent sides u = -2i + 4k and v =i +2] +k Axn pu…

A: We will find the cross product and area.

Q: V9, 0< y< 4 Find the area of the surface generated by revolving the curve x = about the у-ахis.

A: We have to find the surface area.

Q: could you provide an example please?

A: Let us take:  u→=0, 0, 0v→=1, 2, 3w→=4, 5, 6

Q: Given the functions f(x) = . x + 2 and g(x) = x², determine all values of x for which Ag(x)) =…

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Q: Find the general solution of the following differential equation: (sin x)y' + (cos x)y = ex Then…

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Q: Find the limit. Use T Hospital s cos(x) lim - sin(x) + 1- x- (1/2) os (27) CoS sin(2n) 1- 0.

A: Given query is to find the limit of the expression.

Q: Determine whether converges or diverges. If it converges, find the sum. Paragraph U - Ay + v ...…

A: We have to find out sum

Q: 1.) Evaluate: S sin*xcosxdx 2.) Evaluate: Sx³Inxdx 3.) Evaluate: Sx3*dx

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Q: Q2\Find the point at which the tangent to the curve y = v4x2 +1-2 has its slop 2

A: Tangent to curve

Q: Suppose f is a f(8(x))=2x² and differentiable function where 2x f'(x)=2+ f (x). Show that g'(x)=…

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Q: Match each function with its power series representation. Functions: Power Series: Function 1: 2 1…

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Q: Ise cylindrical coordinates. Evaluate . x dv, where E is enclosed by the planes z = 0 and z = x + y…

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Q: 15 If f(x) 2 sin : then f'(x)

A: We will find f'(x) of the given function f(x)=2sin-1x5 in the following step.

Q: ind the dimensions of the right circular cylinder of greatest volume that can be inscribed in a…

A: The figure inscribed in the sphere is needed to be maximized. So, volume of cylinder is to be…

Q: 1. The position of a particle is given by the function s(t) = t* – 32t where t is measured in…

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Q: 6) Let sin 0 - for n <0 < Find the exact value of: %3D 2. a) cos 0 b) tan 0

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Q: For the cost function below, where C is the cost of producing x units of a product, find the…

A: Given query is to find marginal cost function.

Q: Tell if the piece-wise function is continuous on the given interval. Put a CHECK MARK AFTER the…

A: Given graph,

Q: The figure to the right shows the area of regions bounded by the graph of f and the x-axis. Evaluate…

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Q: answer does not exist, explain why. x - 1- V3x +1 a. lim- х — 5 1- x b. lim (x – 6)²

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Q: 3. (Extra) The Department of Health in a developing country has issued a warning that the number, N,…

A: Given problem:- The Department of Health in a developing country has issued a warning that the…

Q: Step 4 Since u = 6 – 4x, then converting back to an expression in x we get the following. (Remember…

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Q: Solve the differential equation: xy' – y = 2x Inx 1.

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Q: Determine whether the function is continuous at the given points. x+2 if x22 : 2,0 x if x<2 f(x) =…

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Q: A region is enclosed by the equations below. y = cos(3z), y = 0, x = 0 6 Find the volume of the…

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Q: can you explain the whole process, step-by-step? like in an essay type. how did they find the first…

A: Here the question is to find the first and second derivative of the function f(x) = 12cos2x. To find…

Q: If the change of variables u = x -2 is used to evaluate the definite integral f(x) dx, what are the…

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Q: Fundamental Theorem: 2x sin t -dt. Find the value of f'(x). t2 +1 Let f(x) = | %3D

A: We can solve this as follows:

Q: x3 Evaluate J (3-2x) using substitution

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Q: 52.8706e-0.3277t h'(t) - (1 + 2.449e-0.327M;2 hes/year, where the child's height h(t) is measured in…

A: Given :

Q: Find y subject to the given conditions. y"= 12x, y"(0) = 14, y'(0) = 4, and y(0) = 4

A: To find y subject to given conditions.

Q: s+13 Find the inverse Laplace transform of s2-6s+34

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Q: Solve inital Value Problem

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Q: f(x)=x^3+6x^2−63x+6 A. interval [-8,0] 1.Absolute Max= 2.Absolute Min=  B. interval [-5,4]…

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Q: 2.7 Given the function f(x) = r²e, Determine the open interval(s) where the functio

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Q: Use symmetry to evaluate the following integral. 1 (6-x) dx | -1

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Q: 1)2xsin-13x

A: Given     write

Q: b) Evaluate d. dx = dt Jo

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Q: What is the radius of an expanding circle at the moment when the rate of change of its area is…

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Q: 1. The planes defined by the equations x + 2y – 2z = 3 and 2x + 4y - 4z = 7 are parallel. Find a…

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Q: 8. Given, h(x) = 2 – x and g(x) = -x²+ 4 a) Plot the two functions on the same graph for -2 < x <4…

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Q: Find solutions of the following equations by the method of separation of variables: 4. 2+= 0 at xe,…

A: 5.

Q: Suppose that f(x)=2x^−4+5x^−2 Evaluate each of the following: 1. F' (2)= 2. F' (-1)=

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Q: Find the domain of r(t) and the value of r(t,). NOTE: Round your answer to two decimal places when…

A: Domain