3. Find the Laplace transform of the piecewise function 03

Q: Evaluate the integral. P(p + 6)°dp P(p + 6)°dp =

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Q: Consider the coordinate vectors 6. (w]s= (als= (B]s %3D %3D %3D 3 4. (a) 8)}. w = (?, ?, ?) (b) Find...

A: Solution: b) S = {x2+1,x2 - 1, 2x - 1} and coordinate of q w. r. to s is  {2,0,4}

Q: Question 7 Suppose that f is differentiable on (-o, 00) and f(-1) = 3. If f'(t) >-5 for all te R, th...

A: Lagrange’s Mean Value Theorem : Let f be continuous over the closed interval [a, b] and differentiab...

Q: Describe in words the region of IR^3 represented by the equations or inequalities. y^2 + z^2 = 16

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Q: 3 y" + 5y" + 6y" + 5y' + 3y = 0 %3D

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Q: 2x dx 67. 4

A: ∫xn dx = xn+1n+1+C ∫f(x) ± g(x) dx = ∫f(x) dx ±∫g(x) dx ∫a f(x) dx =a∫f(x) dx

Q: Evaluate the integral. sec (5x + 8) tan (5x + 8) dx

A: ∫ sec5x+8tan5x+8dx

Q: Solve the differential equation. dy = 3x?cos? y xp Oy = x³ +C O y = tan'1 (x² + C) O y- tan (x³ + C)...

A: topic - differential equations

Q: Use substitution to find the indefinite integral. 6x+7 (3x? + 7x) ... Describe t most appropriate su...

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Q: How would I write six different iterated triple integrals for the volume of the tetrahedron cut from...

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Q: Determine which of the following equations is correct. = xp Sx O +C ㅇ중 Inl +C 2in lal +C O 4x In Ixl...

A: The given integral is  x∫ 14x dx

Q: y=sin

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Q: The graph below shows a transformation of y= 2". Write an equation of the formy= A 2" + k for the gr...

A: topic - transformation of a function

Q: A formula for a function y = f(x) is f(x) = 4x°. Find f(x) and identify the domain and range of f(x)...

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Q: y? at (8, 4) xy Find the slope of the tangent to the curve dy da

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Q: The work W (in joules) done when lifting an object varies jointly with the mass m (in kilograms) of ...

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Q: Consider the following. y = 9 cos“(x), y= -9 cos“(x), -x/2 s x sa/2; about x = R (a) Set up an integ...

A: Given that,  

Q: Compare the graph of n = - 1 with n(x)=x². -J(9 +지은- 1 1 shifts left 36 units, shifts upward 1 units...

A: topic - transformation of a function

Q: dx %-D5 when x= 4. dt ,3 Assume that x x(t) and y y(t). Let y=x +2 and dy when x= 4. Find dt dy (Sim...

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Q: Calculate M6 for f(x) = v6x over [3, 6]. (Use decimal notation. Give your answer to two decimal plac...

A: The function isf(x)=6x over [3,6].The number of sub-intervals is n=6.

Q: Evaluate the integral. (Hint: rewrite cot, do u-sub) R/8 4 cot (40) de n/16 In 2 2 In 8 2 O In 2 In ...

A: Given definite integral can be solve using substitution method . 

Q: Use substitution to find the indefinite integral. ((8+3 In x² xp- Describe the most appropriate subs...

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Q: Verify that fy =f for the following function. %3D f(x.y) =*y+5

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Q: Determine the x-intercept(s) of the quadratic function f(x)=x²+ 2x+ 2. no x-intercept(s) (-7, 0), (–...

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Q: Given K= (-2,-1), L=(2,4), M= (-3,-1) and N= (1,4), Prove that KĽ and MN are equivalent by Showing t...

A: Two vectors are Equivalent if they have same magnitude and direction.

Q: Two variable quantities A and B are found to be related by the equation given below. What is the rat...

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Q: Find an equation of the tangent line to the graph at the given point. 3(x2 + y2)2 = 100(x? – y2), (-...

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Q: 1 (8n – 1)? n=1 a) Enter an integral whose convergence or divergence is equivalent to that of the gi...

A: Given that∑n=1∞18n-12a. Integral test for convergence or divergence fx=18x-12a=1,b→∞∑n=1∞18n-12≈∫1∞1...

Q: Find an equation of the tangent line to the graph at the given point. (x + 2)2 + (y – 3)² = 37, (-3,...

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Q: Ssin(/x)dx Evaluate: None of the given Choices 2 sin(/x)+2/xcos(/x)+C 2/x sin(x)+2cos(/x)+ C D2/xsin...

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Q: What is the direction of the given vector? v= (3,-4). 360 30 or will always be t- you U is it 18O- o...

A: Topic:- vector algebra

Q: Find two vectors in opposite directions that are orthogonal to the vector u. (The answers are not un...

A: In this question we have to find orthogonal vector to given vector.

Q: 2. Find the polar forms of e .of 1+i

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Q: A particle moves according to a law of motion s = f(t) = - 15t2 + 72t, tz 0, wheret is measured in s...

A: As per the guidelines, I can answer maximum three subparts of a question. Since you have asked for m...

Q: 12w3+6w2-5w+1 h : 5w+3

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Q: Laura borrowed a total of $25,000 from two different banks to start a business. One bank charged int...

A: Total money borrowed=$25000first bank chaged 5% simple interest.second bank charged 6.5% interest.ti...

Q: (a) The region in the figure is rotated around the x-axis. Using y = -a? + 6x 9 the strip shown, wri...

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Q: Use Newton's method to attempt to find a solution for the following equation by starting with a valu...

A: In this question we have to find the root of equation with Newton method.

Q: Suppose you know • lim f(æ) = o and lim g(x) = o. • lim f'(2) = - 4 and lim g'(x) = 7 %3D * 00 2 109...

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Q: (3) A firms production function is Q(L) =15L -0.12', where output (Q) is a function of a single inpu...

A: The given function of production is: Q(L)=15L2-0.1L3 where L is labour (number of workers).

Q: Solve the following initial value problem. = - 4cos(2t + x), s'(0) = 300, s(0) = 0 dt? (Type an exac...

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Q: Solve the linear differential equation of order one 2x(y−x^2)dx+dy=0

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Q: Let f(x)= x/x-2.Show that there is no value c ∈ (1, 4) such that f'(c) = f(4)−f(1)/4−1.Why is this n...

A: Given: f(x) = x/(x - 2) Show that there is no value c ∈ (1, 4) f'(c) = f(4) − f(1)/(4 - 1) If f(x) i...

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list.) f(x) = 5x...

A: function  fx=5x2-6x, find the critical points?

Q: If lim f(x) = 9 and lim g(x) = -4, which of the following is true? %3D a. limif(x) + g(x)} = -5 b. l...

A: 1) Given that limit of f(x) at x=2 is 9 and limit of g(x) at x=2 is -4, then we have to find correct...

Q: Given the tabulated function 3 y=f(x) Use least squares to fit the data to a function of the form f(...

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Q: If two perfectly rational players play the following zero-sum matrix games, what strategies will the...

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Q: A.Test the continuity of the given functions. 1. f(x) = (x2 + x –- 6)/(x- 2) 2. f(x) =(x2 – x– 2)/(x...

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Q: Find the area bounded by y = x^2 -1, and the line y = 3. * 31/3 sq. units 35/3 sq. units O 37/3 sq. ...

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Q: Solve the initial value problem. ds = 12t(3t² - 1)°, s(1)=7 dt The solution is s =

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