Find the limit. lim X-X lim X-8 sin 6x 5x sin 6x 5x = (Simplify your answer.)

Q: Use the Laplace transform to solve the given initial-value problem. y" + 8y' + 7y = 0, y(0) = 1,…

A: Let's solve initial value problem by using laplace transform.

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

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Q: If the work required to stretch a spring 2 ft beyond its natural length is 12 ft-lb, how much work…

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Q: (a) AB-BC (b) projABAC (the vector projection of AC onto AB) (c) the area of AABC

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Q: 2. A ball travels in a circle at 3 radians/s and starts on the positive x-axis. How far away is the…

A: Let 'w' be the angular speed of the ball travels in a circle.  Thus, w= 3 radians/s.  Let 't' be the…

Q: Write the first-order differential equation in standard form. (Use yp for dy/dt.) dy dt = 2y + ty +…

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Q: Verify the Divergence Theorem by evaluating F.NO N ds as a surface integral and as a triple…

A: To verify the divergence theorem. And to evaluate the surface integral.

Q: For u(x, t) = f (x + ct) + g (x – ct), where c is a constant, find ux, ut, uxt . Show your work…

A: Given, u(x, t) = f (x + ct) + g (x – ct)

Q: nition 7.1.1. DEFINITION 7.1.1 Laplace Transform et f be a function defined for t > 0. Then the…

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Q: 1. (2x^²+4x-3)abc 2x+4+2+C x

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Q: b. dP = √Pt, P(1) = 2 dt

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Q: Find the critical numbers of the function. f(x) = 7x² - 4x Step 1 To find the critical numbers of f,…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: 2x-4 x²-4x+3 1. Express the function f(x) fractions. Find the interval of convergence. = as the sum…

A: Here, the given function is: f(x)=2x-4x2-4x+3

Q: defferentiate the function: y= ln((x^1/3)/(2x+1))

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Q: (2xcot(x) csc²(x)) dx

A: Given problem:- ∫2xcotxcsc2xdx

Q: Write the function in terms of unit step functions. Find the Laplace transform of the given…

A: ft=t,0≤t<70,t≥7

Q: dr Let A be the area of a circle with radius r. If dt = 2, find dA dt when r = 1.

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Q: solve by hand( numerically) f(x)= cos(x)-x exp (x) using the bisection method and Newton- Raphson…

A: Let f(x)=cos(x)-x exp(x). Here f(0)=1>0 and f(1)=-2.178<0 Now, Root lies between 0 and 1.…

Q: State the equation of a relation whose vertex would be lower than the origin and to the left of the…

A: We have to find the equation of the relation whose vertex is lower than the origin and left to the y…

Q: Give the applicable trigonometric substitution formula for S A. x=2 sin 0, dx = 2 sec ² 0 de B. x…

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Q: Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line.…

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Q: 2 f(t) = 2t² - 1, [3, 3.1] Compare this average rate of change with the instantaneous rates of…

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Q: In the following exercises, use direct substitution to show that each limit leads to the…

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Q: Use the Root Test to determine if the given series converges absolutely or diverges. ∞ Σα 1 ( 9) n…

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Q: 7. -In2 2ex ex + 1 - dx

A: As per bartleby guidelines we only give first question answers.  Please repost for other parts.

Q: 24. Differentiate each of the following with respect to x. Simplify fully when indicated 1 (a)_y=x²³…

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Q: tf(x) be a function defined on [0,8] whose derivative has the following graph: Figure 1: Graph of y…

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Q: Consider the following. f(x) = tan(x), (-1) (a) Find an equation of the tangent line to the graph of…

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Q: Determine the limit of the given sequence: sin (159) an = If the limit does not exist, enter Ø. If…

A: Use limit

Q: Find an equation of a line that is tangent to the graph off and parallel to the given line. Function…

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Q: Question Consider the function f(x) = . (z+9)(z-2) 2+3 What are the x-intercepts? Write your answer…

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Q: ate algebra and Theorem 7.2.1 t 3s 10 s² + 25.

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Q: Tutorial Exercise Find the derivative by the limit process. f(x) = 14 - x² Step 1 Complete the…

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Q: 2. Find the area enclosed by T = @ cos 30-

A: We need to find area.

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = (et-e-t)² L{f(t)}:…

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Q: Ise appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: 3) . Is the differential equation linear? y' = y + ey YesNo       PLEASE SHOW STEP BY STEP .

A: answer is in next step. please give a like !!

Q: 2. π 2 1/² cott x dx 4

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Q: maximum

A: if you specifically asking to how to find maximum and minimum value. Please refer to the image below…

Q: Find the nth term of a sequence whose first several terms are given. 3, 5, 3, 5, 3, 5, ... an =

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Q: Determine the explicit formula for the n-th term of the sequence written below. Note that the first…

A: I am attaching image so that you understand each and every step.

Q: Consider the following given function and given interval. f(x) = 10 sin(x) - 5 sin(2x), [0, π] (a)…

A: Given data÷ fx=10sinx-5sin2x Interval : 0,π   From part a) the value of favg=20π   fc is given by…

Q: if the limit at infinity exists find the limit lim(inf)=3x^3+5x/4x^4+10x^3+2

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Q: 2 (6 4t+3)

A: answer is in next step. please give a like!!

Q: 9. A missile is rising at a constant rate of 100 meters per second. An observer is 600 meters away…

A: Given speed of the missile is 100meters per second. an observer is 600 meter away from the launching…

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: 17. Find the linear function f(x) that is parallel to 4x + 3y = 6, such that f(0) = 7.

A: Given function, 4x+3y=6, That is 3y=-4x+6 y=-43x+2 compare to y=mx+c Therefore m=-43

Q: ds" Evaluate the given Laplace transform. (Write your answer as a function of s.) L{te-15t}

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Q: Use inscribed and circumscribed rectangles to find the area of the region to the right of the line x…

A: Concept: the area between the region y=f(x) and ==g(x) on the interval [a, b] Let us assume that…

Q: Consider the following. Differential Equation dy=-10xy dx (a) Use Euler's Method with a step size of…

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