by defintion the Laplace transform of a function f(t) is an improper integral of the form F(s) = √°* e-stf(t)dt. Use the improper integral definition of the Laplace transform to calculate the Laplace transform of f(t) = 2t³.

Q: Find the derivative of the function. 3 y' = y = x² + 8 x² - 8 -96x- x² +8 2 4 x²-8 2 X

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Q: Let f(x)=√71-x The slope of the tangent line to the graph of f(x) at the point (7,8) is The equation…

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Q: (FRQ No Technology) The graph below represent f'(x), the derivative of f(x) on the interval [-4,6]…

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Q: Find the derivative dw dt dw dt 2 where w = 3xyz, x = 5t³, y = 2t 1, and z = 4ť ².

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Q: Find the domain and all critical points in the domain of y = 1- x² is help (intervals) a. Domain of…

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Q: 1 Find the area between the graph of x = y² and the y-axis on the interval [1,4]. -0.5 4 3 2- 1 0 Y…

A: to find the area between the curve x=1/y^2 and y axis in tge interval [1,4]

Q: Use the given graph of the function g to find the following limits (Note that if a limit does not…

A: Using the given graph we can find all the required limits

Q: Answer the following True or False. Sa 1 CSC x dx = ln(cscx) + C O True O False

A: The given problem is to identify whether the integral  trigonometric expression is true or false.

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Q: Find the derivative of the function. y = Xx x + 3

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Q: Given the function graphed below, evaluate the definite integrals. -1 0 4 3 2 1 -1 -2 -3 -4 1 f(x)dx…

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Q: Kindly provide, using the graph: a.) domain and range in interval notation. b.) the interval for…

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Q: Let f(x) = {(x²-1) x²-x+k₁ ifx <₁; ifxzi kan find the limit of f(x). (1) lim, ₁- f(x)= 1 (ii) lim +…

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Q: y" +9y = 2x²e³x +5

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Q: 1. Convert radians/degrees and find the coterminal angles between 0-360° or 0-2r radians. a) 13n/6…

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Q: An angler hooks a trout and reels in his line at 3 in./s. Assume the tip of the fishing rod is 11 ft…

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Q: Label the points A, B, C, D, and E based on the continuity and differentiability of the graph at…

A: Using given graph we can identify the points of continuity and differentiability

Q: Find the limit. sin(0) lim 0-00+ tan(0)

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Q: A farmer has 225 yards of fencing to form two identical rectangular pens and a third pen that is…

A: A farmer has 225 yards of fencing to form two identical rectangular and a third pen that is twice as…

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Q: If f'(x) = (2-2x)e(1-x), which of the following statements is true about the graph of f(x)? Select…

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Q: differentiable functions f and g are defined for all real numbers x. Values of f, f, g, and g' for…

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Q: find the value of the constant A SO that y= A sin 3t satisfies the differential equation y² + 2y = 5…

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Q: Answer the following True or False. [6³dx = da 6 + C In 6 O True O False

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Q: A region bounded by fly) = y, y = 2, y = 6, and x = 1 is shown below. Find the volume of the solid…

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Q: A conical tank has height 3 m and radius 2 m at the top. Water flows in at a rate of 1.3 m³/min. How…

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Q: The graph of f'(x) is given below. Use this graph to determine the intervals where f(x) is…

A: to evaluate the increasing and decreasing intervals of f(x) when given graph of f'(x).

Q: < Consider the surface z = f(x,y)=√1-x² - 2y² and the oriented curve C in the xy-plane given ¹,…

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Q: True or false and why? Explain. The linearization of f(x,y) = 5 + 7x + 3y at any point (a,b) is the…

A: To determine whether the following statement is true or false.The linearization of at any point is…

Q: Natalie and Shannon start from point A and drive perpendicular roads AB and AC, respectively, as…

A: Speed of lara is 45 km/hrspeed of shelia is 40 km /hrShelia starts one hour before lara

Q: 2. Find sin(A) and tan(B) using the right triangle below. B 11 6

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Q: Find an equation of the tangent line to the curve at the given point. y = xe−x2,    (0, 0)

A: Given, ,  point is (0,0).

Q: Draw a graph to match the description given. G(x) is increasing over (-∞,2) and (8,00) and…

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Q: Which of the following is the correct form of the partial fraction decomposition of x4 -? x4-1 A.-1+…

A: Let A=.Formula of partial fractions decomposition

Q: Answer using the following polynomial using remainder theorem. Show your solutions. f(x) = 4x5 -…

A: To answer the following polynomial by using remainder theorem.

Q: K Find the first and second derivatives. 6 X dy dx y = 5x-5 11 d²y dx² ||

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Q: 6. Find the sine and cosine of the angle that the point (3/5, 4/5) on the unit circle makes with the…

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Q: If a ball is given a push so that it has an initial velocity of 7 m/s down a certain inclined plane,…

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Q: P(x) = F(x)G(x) and Q(x) = Find P'(2). y 6 5 4 3 2 1 1 1 2 F(x) G(x)' where F and G are the…

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Q: 1. Evaluate LL2 cos (1-4) dy da (v 2x dx. 3

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Q: 15. Answer the following questions about tangent lines. a. b. C. Find an equation of the tangent…

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Q: Let F(x) = f(f(x)) and G(x) = (F(x))² and suppose that Find F'(3) and G'(3). F'(3) G'(3) = = f(3) =…

A: Given,  F(x)=f(f(x)) and .Given, f(3)=9, f(9)=3, f'(9)=4, f'(3)=15

Q: et C be the curve y=x² for 1 ≤x≤ 3, Evaluate 8xds с 3 2 2 A. 3 (17 ³ - 5 *) B. 3 (37²-5) c. 3 (5³…

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Q: For this system of linear equations, find the general solution of the system or state that the…

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Q: (c) Does the volume of the cylinder of part (b) increase or decrease as t increases? (a) Find V'(t).…

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Q: Evaluate the integral [(2x + 7)(x² + 7x + 2)² dr by making the substitution u = x² + 7x + 2. + C…

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Q: Find the derivative of the function. y = cot² (sin 8) ||

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