Differential Calculus Find the third derivative of the ff: 1) y x 1-ex 2) y = 2ex - 8x 3) y = 6ex - 7x

Q: Find the solution of the following differential equations. Show your solutions 6. (D6 + 3D + 3D² +…

A: To find the soution of the following differential equation.D6+3D4+3D2+1y=0

Q: Consider the function y = g(x) y = g(x) = -x ² + 2x + 7 9x of the the limit definition to compute a…

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Q: Direction: Differentiate the following X 1. y = ₁ = ex 1 - 2. y = 6ex - 7x 3. y = 1+5x Inx

A: To differentiate the following.1 y=x1-ex2 y=6ex-7x3 y=1+5xln x

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.…

A: To solve the following integral

Q: The sum of two numbers is 18. Find the smaller number if the product of one of the numbers to the…

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Q: What is the area bounded by y = 0, y = eˣ, x = 0 and x = 1?

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Q: What are all of the solutions to the equation (cos 30)(cos ) + 1 = (sin 30)(sin 9)? R T ==+= 4 2 0…

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Q: Find all solutions of the following linear system: 4x+8y-12z 2x +2y-2z 5x -5y-5z = 0 = 0. = 0

A: To find all solutions of the following linear system.4x+8y-12z=02x+2y-2z=05x-5y-5z=0

Q: 2. Given x³ + y³ = 3xy, find the equation of the tangent line at (2/3,4/3). I'm looking for your…

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Q: The normal line at x = 1 of the curve y=x²+x+ where m = 2 and n = 3, interects the curve at a second…

A: The normal line at x=1 of the curve y=x2+mx+n, where m=2 and n=3, intersects the curve at asecond…

Q: 01 3 2 16-s² ds= (Type an exact answer.)

A: We are required to evaluate∫04316-s2ds

Q: Use logarithmic differentiation to determine y'(x) when Select the correct answer below: O y'(x) = O…

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Q: Find the following for the given equation. r(t) = (t² + 3t)i + (t²- 3t)j (a) r(t) = (b) r"(t) = (c)…

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Q: 2. When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.01…

A: Given: Rate of increase of radius = 0.01 cm/min Radius = 50 cm

Q: (E) What is the form of the general solution to this differential equation?

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Q: Which one of the following integrals gives the length of the parametric curve x(t) = t², y(t) = = =…

A: As we know that length of the curve from a to b  L = ∫ab( dxdt )2 + ( dydt)2dtGiven  x = t2y = 2t 0…

Q: Find the compound amount for the deposit and the amount of interest earned. $7000 at 7% compounded…

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Q: Find the approximate increase by the use of differentials, in the volume of the sphere if the radius…

A: Let radius of sphere=r units

Q: e the equation subject to the given conditions d'y dy 5 dx² dx 2 +6y=4e², y(0)=2, y'

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Q: Find dx dx 2x r = f cos (?)dt 11

A: y = ∫x2πcos( t2 )dtwe want to find out dydx= ddx∫x2πcos( t2 )dt

Q: Please answer b and 7 : )

A: We need to create volume problem.

Q: Let f(x, y) = x¹ y ¹ (x² + y²)³° Show that lim f(x,y) does not exist. (x,y) →(0,0)

A: Let f(x,y)=x4y4(x2+y4)3  We  have  to show that lim(x,y)→(0,0)f(x,y) is does not exist

Q: Kate starts a new business manufacturing bobble-head figures of Eagles players. Her initial cost is…

A: To solve the following problem

Q: Find f(₂ + 2)(x - 7)dx + C

A: The given integral is: I=∫x+2x-7dx   As we know that, The Sum Rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power…

Q: Jse Newton's method to approximate a root of the equation 4x³ + 8x + 2 = 0 as follows. et x₁ = − 2…

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Q: Where on the interval [0, 7] is the secant line parallel to the tangent line for y = x sinx?

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Q: Find the solution of the following differential equations. Show your solutions 3. (D³3+8)²y = 0

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Q: Do not use a calculator for this problem. Find the x-value where the maximum value of y = sin x 3x²…

A: We have to find the x-value where the maximum value of y = sin x- 3x2 occurs.

Q: The length of the arc of y = ln cos x from x = π/4 to x = π/3 equals______.

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Q: Compute the curl of the following vector field. 2 2 F = (x² - y²,5xy.4z) The curl of F is (i+j+ k.

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Q: Vector v is shown in the graph. S T (-3,4) 7 Ov = (-3, 4); ||v|| = -5 O v = (3, 4); ||v|| = -5 Ov =…

A: Given:

Q: How long will it take $3,000 to grow to $25,000 if it is invested at 7% compounded monthly? years…

A: Given: Initial amount, P=$3000 Final amount, A=$25000 Rate of interest, r=7%=0.07

Q: Let z = √xy + 2x²y³. The slope of the line tangent to the curve of intersection of the surface given…

A: The surface given is  z=xy+2x2y3

Q: 806 Chapter 14 Multiple Integrals It does not apply to regions with complicated holes through them,…

A: Let's find radius value.

Q: ar(t) = cos(-10t)i+sin(-10t)j-10tk, compute A. The velocity vector v(t) = B. The acceleration vector…

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Q: Find the series' radius of convergence. (x-2)" Saman Σ An=0

A: Given series:- ∑n=0∞x-2nn58n

Q: z = 8x² + 8y² + 18 nearest the plane 8y - 3x - 7z = 0.

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Q: y that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then…

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Q: If 4 + 2i is a zero of a function, what other zero will the function also have? O2+i O 3-i O 2-4i O…

A: The answer is given below:

Q: (a) (उ, म ) |

A: Given  a .

Q: 6. A hemispherical water tank, shown below has a radius of 6 meters and is losing water. The area of…

A: Given A = 12πh - πh2where h = depth at a time , h = 3 meterA = area Given dhdt = -12meterminwe want…

Q: Differential Calculus Direction: Differentiate the following trigonometric functions: Part I. 1) y =…

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

Q: Find a number & such that f(x) - 3| < 0.2 if x + 1| < 6 given f(x) = 2x + 5 Leave the result as a…

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Q: S* (x² − 4x + 4) dx ≥ 0

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Q: Two particles travel along the space curves r(t)and u(t). A collision will occur at the point of…

A: Two particles travel along the space curves rt and ut. A collision will occur at the point of…

Q: 7. Using Reduction of Order: (D² - 1)y= 2e²x 8. Using Reduction to an equation whose Right Member is…

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Q: What are the magnitude and direction of w = (-5, -14)? Round your answer to the thousandths place.…

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Q: Evaluate the given Laplace transform L{t² *te¹} a. b. C. d. -2 (S-1)²s 2 (5+1)²5³ 1 (S-1)s³ 2…

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Q: The topic is linear differential equation, answer should have the equation and the general solution

A: Please seethe below answer.

Q: Determine the interval of convergence of the power series. (4x)k k! Σ k=0 O A. (-00,00) O B. (-4,4)…

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