Use the method of Laplace transforms to solve the given initial value problem. Here, x' and y' denote differentiation with respect to t x-x-y 1 x(0) = 0 -x+y'-y 0 y(0) = - Click the icon to view information on Laplace transforms. X(1) = Y(t)= (Type exact answers in terms of e.)

Q: Decide whether the function f(x) =7x -5 is a probability density function on [- 1, 1]. If not, tell…

A: Topic:-  probability

Q: :-1 and g(x) = "- Vx +1 Let f(x)= arccos 2arctanx. (a) Find f'(x) and g'(x). V-1 *-2 arctan Vx ?…

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Q: Solve the equation. Write the solution set with the exact solutions. Inx+In (x-3)%= In(5x-7) If…

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Q: PQ1

A: Given, f'(x)= cubic function  We know that, If we take the derivative  of the given function, We…

Q: Find the rate of change of the function at a given value. 1. f(x) = 2x – 3, at x = 5 2. f(x) = 2x² ,…

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Q: Find an equation in rectangular coordinates for the curve 2r2 = cos (20). (Express numbers in exact…

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Q: Consider the following lines 4:z=1,y-1=-4,2=1-3t :z=28+1,y=1-3s,2=1 -y+1 %3D z-1 3a 2a 3 Find the…

A: Explanation of the answer is as follows

Q: Given the sequence {un} with: п — 3 Un ,n > 1 5n + 1

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Q: 3. -1 1 2 3 4 5 6 7 +1

A: To approximate the area under the curve graphed below from x=2 to x=5 using a Left Endpoint…

Q: y as a one-to-one function of x.

A: The given graph is:

Q: Does the following series converge or diverge? (2n)! Σ 6"(n!)? n= 1 O The series converges. O The…

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Q: A 1+ 2 + 3 + 4+ + 127 Σ > B, where .. n=1

A: First trace the rth  term then use the summation notation.

Q: 2. The projected rate of increase in enrollment in a new college is estimated by the expression dE =…

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Q: (a) Find the MacLaurin polynomial of degree 9 for the function h(x) = ln(1 + x3). (b) Use you answer…

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Q: Find the particular antiderivative that satisfies the following conditions: dx/dt=8e^t−7;…

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Q: Tom is running along a circular track that has a radius of 51 meters. Tom starts at the 3-o'clock…

A: Given information: ------------------------------------------------------------------------------…

Q: Evaluate the definite integral (18z 4x +3) da 4

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Q: Evaluate the line integral L(a - )da + (1 + y° + æ")dy, where Cis the circle of radius 2 centered at…

A: We have to evaluate the integral.

Q: Test the series for convergence or divergence. -1 sin? n n+ 37

A: Given

Q: The total cost of producing x instruction manuals is given by the function C(x) = 800 + 27x – 0.6x?…

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Q: Test the series for convergence or divergence. n=1 n35n (n+ 2)!

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Q: 4. (2x2-у?)dx+2хydy-0

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Q: Find the Taylor polynomial of degree four for the function f(x) = e at x = 0. The Taylor polynomial…

A: The given function is:…

Q: 2. Let f be continuous and differentiable everywhere. Suppose that f has zeros at 1 and 3. Show that…

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Q: S x²(csc2x³)(cot2x³)dx

A: Given ∫x2csc2x3cot2x3 dx To evaluate the integral:

Q: 85 2 1 r³)(1 x2 O A. (3x? – 2+ 3 - O B. 85 2 1 (3x2 – 2+ -x3)(x+ 3 · (1 – →)(x³ – 2æ + 17x3) 85 2 1…

A: Given query is to find the derivative using product rule.

Q: Find the exact arc length of the curve x ² + 2) from y = Oto y = 5. Enter the exact answer. L =

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Q: Verify that the two planes are parallel. -x + 6y + 3z = 7 1 --x+2y +Z 8 Find the normal vector, n,,…

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Q: diverges: 3n/22n-4=27/4+81/16+243/64+729/156

A: Given query is to find series converges or diverges.

Q: --6 lim sin (9x)

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Q: Does the following series converge absolutely, converge conditionally, or diverge? (-1)" Σ 3/2 +4…

A: The given series is ∑n=1∞-1n7n32+4. Note that, The series ∑n=1∞an is said to converge absolutely if…

Q: xp- to within 10-4 of its actual value. Please show all Approximate 2+ x steps.

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Q: Find the equation of the plane through the point P = (5, 3, 3) and parallel to the plane 3y – 5x –…

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Q: In Jx2/25+ x² dx , we let x= 5sine. A True B False

A: Note Since you have asked multiple question As per our policy, we will solve the first question for…

Q: Approximate the area under the curve y=x^2 from x=1 to x=4 using a Right Endpoint approximation with…

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Q: Find the vector equation for the line of intersection of the planes 2x – 2y – 5z = 5 and 2a + 2z = 1

A: Given  equation of planes 2x-2y-5z=5 2x+2z=1

Q: Find the point where the function f(x,y,z) = x + 2y + 3z subject to the constraint xyz= 2 takes on…

A: Answer is in below steps.

Q: Find the Maclaurin polynomial of the ninth degree for the function h(x) = ln(1+x3)

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Q: Determine the interval(s) on which the vector-valued function is continuous. (Enter your answer…

A: The vector-valued function,    r(t)=ti-t-3k

Q: 6. The definition of the first derivative is f(x+h)+f(x) E. f'(x) = F. f'(x) h f(x+h)-f(x) h…

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Q: at is wrong with the following equatlon: 8 + (6/2) = 17 -5 %3D A The symbology is not standard so…

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Q: 5. If the population P of bacteria (in units of 1000) is declining because of a toxin, its rate of…

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Q: dx Evaluate: xV x2 + 4 x² + 4 – 4 + C x2 + 4 + 4 - A) 4 x² + 4 – 2 +C x² + 4 +2 Vx² +4-2 + C Vx² + 4…

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Q: nt Use the model A =Pe" or A= P| where A is the future value of P dollars invested at inter %3D…

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Q: Find the area between the curves y = = x² and y = %3D 3+ 2x2 Select one: V2 O a. O b. 2/2 V2 c. 6.…

A: The region is bounded by the curves,   y=x2 and y=23+2x2 Note:      Multiple questions are given, we…

Q: In polar form, the integral (a + y°) dy dæ 9-22 reads 2T 73/2 dr d0 r°dr do ?dr de 0. O None of…

A: To convert cartesian co-ordinates (x,y) into polar co-ordinates (r,θ) we use the following…

Q: QUESTION 2 If a company has a monthly fixed cost of $24,000 and variable cost of $5 each to produce…

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Q: Find u · v, u· u, ||v||², (u · v)v, and u (3v). u = (2, 10), v = (-3, 2) %3D (a) U V (b) U U (c)…

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Q: one-to-one function is given. Write an equation for the inverse function. x-3 t(x) = x+7 () = D %3D

A: Given query is to find the inverse function.

Q: Verify that the values of the variables listed are solutions of the system of equations. fx + y = -5…

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