find the given differential solution, using homogeneous equations with constant coefficients. 6y''-y'-y=0

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Q: Consider the differential equation y" - y' + 3y = f(t), such that y(0)=0 and y' (0) = -9 f(t) is…

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Q: 6) The graph of g'(t) on the interval [0, 10] is shown below. If g(0) = 3, find g(10). g'(t) 4 0 t

A: Let's find value of g(10).

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Q: Find the taylor series of the following functions for the given points:- 2- f(x)= sinx a= π/4 3-…

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Q: Q4\ Find the average value of f(x,y) = (+√) where 0≤x≤y and 0 ≤ y ≤ 4.

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Q: Show that the function f(x, y) = 3x - 4y² is differentiable at point (−1, 2)

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

Q: Matching Type. Match the functions antiderivatives in Column B. Column A 1. f(x-4)³dx 2. f(x + 1)³dx…

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Q: Evaluate: lim (x² + €¯²) (x²¹ cscx) I→0+

A: We will evaluate the given expression using DL hospital rule.

Q: Evaluate the integral. a 6 dx ਚ 2 + a> 0

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Q: Q6. Let w = f(r,0), r = √x' + y³, 0 = tan'(y/x), ), find aw ?х > and ди ду in terms of r and 0.

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Q: 8 What type of association does the following represent: The value of y decreases as x increases A.)…

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Q: 7. Compute the area of the region R enclosed by the curves y = x² - 1 and y = 1- x.

A: We have to find out the area

Q: 3) O 4 N

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Q: Find the equation of the tangent plane to the surface defined by the function f(x, y) = x³…

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Q: Solve the given differential equation by using separable variables. 2. dy y-1 = dx x + 3

A: We will solve the given differetial equation using separation of variables.

Q: 1 1 x² + 1 2 dx

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Q: 2. A particle is moving in space with position function (t) = (sin(3t), cos(3t), 3 – 4t). 2.1. Find…

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Q: Q4: Solve the following integration corrected to 3 decimal places using: 1. Trapezoidal rule 4…

A: Given: ∫154xdx Solution: X 1 2 3 4 5 y=4x 4 22 43 2 45 h=1y0=4y1=22y2=43y3=2y4=45

Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: (a) lim x→0+ (sina) 1 (b)…

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Q: 5 1 1 + 2r dr

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Q: 2 \n'/x/ ax

A: We will solve the problem.

Q: Given g(x) = -10x-2 -5x-2' Provide your answer below: g'(x) = find g'(x) using the definition of a…

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Q: 5. In a room with 10 people, everyone shakes hands with everybody else exactly once. How many…

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Q: Short Answer 11. Calculate X+W for X- 3) 2 and W- or explain why this operation

A: Given X=70-1423 and W=-4111-122To Find:  X+W

Q: find the integral from 1 to 4 of (3t^(3/2) i+(t+4)(√t)k)dt

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Q: Q4) Prove that dx 1+ 2 sin x In tan x 2 tan X + 2√√3 +2 + √√3

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Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

A: Converting into Cartesian form

Q: d/dx [x/(x^2 + y^2) ] = * O [(y^2 + x^2)/(x^2 + y^2)^2 ] O -[(y^2 +x^2)/(x^2 + y^2)^2 ]…

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Q: 7) A can of soda with a temperature of 56 degrees Fahrenheit is placed in a refrigerator which is…

A: Given that, A can of soda with a temperature of 56 degrees Fahrenheit is placed in a refrigerator…

Q: Use Cartesian coordinates to evaluate JJJ² dV D where D is the tetrahedron in the first octant…

A: Given integration is evaluated.

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Q: In 3 2 – sinh x tanh x cosh x dx

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Q: Let F(x,y)=√√y-x, then answer the following ( (1) Find the function's domain (2) Find the function's…

A: According to our guidelines we can answer only one question or three subparts of a question.other…

Q: Question Using the definition of a derivative, find f'(x) given f(x) = -x³+4x² + 4x + 2. (Do not…

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Q: H.W find the first four terms of the binomial series for the functions:- 1-(1-x)-¹2 2-(1+)-²…

A: As per the guidelines I am supposed to do the first question among multiple questions. So here I am…

Q: H.W: Evaluate the integral 30 1. [[(x²y = 2xy)dydx 0 (2x- - y)dydx 2m [[(sinx+cosy)dxdy 3. 5. 2. (x…

A: Since you have posted a question with multiple sub parts, we will solve the first three subparts for…

Q: INSTRUCTIONS: Please write clearly and understandable way. • Write all the corresponding Given with…

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Q: Prove the following using the principle of mathematical induction. For n > 1, 1 1 1 1 = + + + 54 ( –…

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Q: 3 By direct partial integration, Solve the following PDES 8- 8²u axdy = ceBX Cosy SXUCX,#) Ex u(π,…

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Q: dy a. Use implicit differentiation to find dx b. Find the slope of the curve at the given point.…

A: Use derivative of square root of function.

Q: 2. Given the values for f(x) on the table, approximate the area under the graph of f(x) from x = -5…

A: Let's find approximate area under the graph.

Q: Q1.. Find domain and range for following functions: (2 20 a) y = {1x<0 {² D f(x) + D g(x) = D(f(x) +…

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Q: 6 By Separation of variables, Solve the following 5 PDES :- ²4. ²4 0 o 2 dt² dx² u(e,t) = u(5,t) =6…

A: Given

Q: Q3: A) Find the limits below x² + sin²y 1) lim (x,y) (0,0) 2x² + y² 2) lim (x, y)-(1,1) x² - 2xy +…

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Q: Relative

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Q: I. Solve the following integrals completely and honestly. Show your solution in ink and as neatly as…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Exercise (1-3): By Charpit method solve the following PDE Question Answer (1) p²x+q²y=z z =…

A: Application of integration