Solve the problem. Find the area between y = (x - 3)ex and the x-axis from x = 3 to x = 7. A) e²-e³ B) 3e7 C) 3e7+e³ D) e7+e³

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A: We can find the arc length as below.

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Q: 6. Evaluate the following limits: 1/3 (x+8) -2 a. lim X x-0 b. lim x→-3 2 x²-9 2x² +7x+3

A: Given :limx→0x+813-2xlimx→-3x2-92x2+7x+3

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A: Topic:- Algebra

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Q: A) Explain with short examples the algebraic vector properties. 1. A+B=B+A 2. A+ (B+C) = (A + B) + C…

A: To explain with the examples with the algebraic vector properties given.

Q: 5. Let f be a function continuous on R and F(x) = af f(t)dt. Then F"(0) is equal to 0 0 O f(0) ○…

A: Let f be a function continuous on R and Fx=x∫0xft dt. Then to determine the expression for F''0.

Q: Correlational designs have one independent variable and one dependent variable  true or false?

A: Explanation:-  A  dependent variable is the variable to be explained and independent variables are…

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A: We know, ∫dxx-a=lnx-a

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A: Please refer to the image below

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Q: 25- Find the Maclaurin series generated by the following function: f(x) = sinh(x)

A: Above question is solved.

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A: This is a problem related to trigonometric identity. Based on the general formula and concept we…

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A: We have to find the inverse laplace.

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A: Concept: We have a boat on the water, and let the closest point on a straight shoreline be x, In…

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Q: Q4. f(x)=5 and 1(x)de=8 dx = 5 and f(x) dx = 8 then f(x)dx a) -3 b) -13 c) 13 d) 3 dx is given by

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Q: "Si" means "if" The function f is defined as follows: Knowing this, calculate: f(x) = 4x³+ln(3x) si…

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Q: Q3- Sketch the region of integration and evaluate the integral: In8 lny [TD [t ex+y dxdy

A: Given problem:-

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Q: Determine the area of the region bounded by the curves y = ₁, y = 2x and x = 4

A: This is a problem related to integration. Based on the general formula and concept we will answer…

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A: We can solve the given problem by using the variable separable method.

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Q: 1. The graph of y=sin z is transformed so that the transformed image has a period of 4m and a phase…

A: Given problem:- The graph of y = sin x is transformed so that the transformed image has a period of…

Q: Give the Fourier transform of the function f. f(x) ha x € [0,₁] {* otherwise. =

A: Above question is solved.

Q: A rectangle is bounded by the x-axis and the semicircle y = √25-x² What length and width should the…

A: Area of a rectangle is the product of its length and width. We use first and second derivative test…