Solve for G.S / P.S forbthe following differential equations using the method of solutions for linear equations of first order, first degree

Q: Subtract: (x + 2) / (2x - 3) - 4 / (x + 3)

A: We have to subtract the expression x+22x-3-4x+3 Subtracting the given expression. x+22x-3-4x+3=x+3x+...

Q: Use the limit definition to find the derivative of the function. f(x) = x + 3x + 4 %3D f(x + h) – f(...

A: Given that, the function is fx=x2+3x+4. obtain fx+h-fxh. fx+h-fxh=x+h2+3x+h+4-x2+3x+4h=x2+2xh+h2+3x+...

Q: Evaluate the definite integral. Use a graphing utility to verify your result.

A: To evaluate: ∫-11 t2-5 dt To verify result using graph.

Q: Find the particular solution. y' = ex − 8;    y(0) = 9

A: Given, y' = ex − 8  

Q: Partially differentiate the following equations with respect to x1 and x2. Note the superscript stan...

A: Given function is y=5x1+x222 Differentiate y partially with respect to x1 using chain rule of differ...

Q: A particle moves along the curve *= 21² , y = t² – 4t and = = 31 – 5 where t is the time . Find the ...

A: Given: Position vector is given as, r→=2t2i^+(t2-4t)j^+(3t-5)k^ The objective is to find the velocit...

Q: Find an equation of the graph that passes through the point and has the given slope. (Enter your sol...

A: y'=x/18y ,            (0, 2)dydx = x18y18y.dy  =  x.dx         .......................(1)

Q: find x rounded to one decimal  x=

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Q: i)Find the area of the region enclosed by graph of fx=x3-x2 and gx= 2x .

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Q: .2 x +1 Find dy/dx given that y x2 – 1

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Q: Verify that the geometric sum formula gives the correct result for the sums 1 + (1)/(2) and (1)/(2)+...

A: Formula for the sum of a geometric  series:Sn=a11-rn1-r    r≠1a1=the first termn=number of termsr=th...

Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley ...

A: Given : The pulley is 1 m higher than the bow The rate at which rope is pulled dydt=1m/s

Q: Please help answer questions (a), (b), and (c) in the picture picture, showing all work/thinking pro...

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Q: Question 1: Write the following Logarithmic expressions as a sum of logarithms expressing all powers...

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Q: Suppose a certain medication is administered to a patient with the percent of concentration of the d...

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Q: dy Find if dx y = (4x – 4)°(4x² 8. 3x + 2)°

A: y = 4x-46 4x2-3x+28dydx = ?Important points:ddxxn = nxn-1ddxax+bn = nax+bn-1.a×1+0 = anax+bn-1

Q: A rectangle is bounded by the x−axis and y−axis and the graph of y=(6-x) / 2. What length and width ...

A: The area of the rectangle is given by the formula, A=x·y Since the point (x, y) lie on the line so i...

Q: f(x) = eur b. edx + b

A: fx=eax-beax+b (a) For the domain of the function first substitute the denominator equal to 0. eax+b=...

Q: Use the keys on your calculator or graphing utility for converting an angle in degrees, minutes, and...

A: To Determine: Use the keys on your calculator or graphing utility for converting an angle in degrees...

Q: Find the critical points of ƒ(x) = (x2 - 3)ex. Identify the open intervals on which ƒ is increasing ...

A: Given        f(x) = (x2-3)ex

Q: Find the average value gave of the functiong on the given interval. g(x) = 4/x, [1, 27] 9ave

A: The formula for the average value of the function gx over a given interval a,b is, gave=1b-a∫abgxdx ...

Q: A ladder leans against a vertical wall. If the top of the ladder slides down at 4 ft how is the sec ...

A: Let x and y (in feet)be the distance of bottom of the ladder from the wall and distance of the top f...

Q: a. Determine whether the Mean Value Theorem applies to the function f(x) = In 8x on the given interv...

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Q: Factor​ P(x) into linear factors given that k is a zero of P.P(x)=x3+7x2+7x-15; k=-5The factorizatio...

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Q: f(r + h) – f(x) First, find h Preview Next, simplify the numerator. Preview Divide out the h. Previe...

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Q: The radius of a sphere is increasing at a rate of 4 inches per minute. Find the rate of change of th...

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Q: Find the values of x for which the series converges.

A: Given information: ∑n=0∞x-35n The series is converges

Q: I need help solving this question.

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Q: Evaluate the following integrals using theFundamental Theorem of Calculus.

A: Given: I=∫0π4secxsecx+cosxdx for finding given integral, first we simplify given expression then int...

Q: Absolute maxima and minima Determine the location and value of the absolute extreme value of ƒ on th...

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Q: Use integration to find the general solution to each differential equation. (Use C for the constant ...

A: Consider the given differential equation, 8ydy=40xdx use the formula of integration, ∫xndx=xn+1n+1+c

Q: Complete each statement and name the property of real numbers you have used.(a) ab=________ ;_______...

A: aab=ab=baCommutative property of multiplication.ba+b+c=a+b+c=a+b+cAssociative property of additionca...

Q: Find the limit, if it exists.

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Q: Complete the following steps for the given function ƒ and interval.a. For the given value of n, use ...

A: Given fx=cos2x,    on 0,π4 , n=60  part a: The length of each subinterval is, ∆x=b-an since n=60 , a...

Q: Find an equation of the tangent line to the curve y= 10xat the point (1, 10).

A: Given: y=10x for finding tangent of given curve at given point we need slope m of tangent at given p...

Q: Make a sign diagram for the derivative of the rational function. f(x) = 6/(x+3)   Undefined X = ?

A: Given function, fx=6x+3

Q: Please help me with this question. Thank you!

A: Since you have asked multiple questions in single request  so we  will be answering only first quest...

Q: Find two positive numbers so that the sum of the first and twice the second is 100 and the product i...

A: Let two positive numbers are x and y. Given that the sum of the first and twice the second is 100 . ...

Q: Use the product and/or quotient rule to find the derivative. f(x) (2x+1)(2x +3) %3D f'(x) = Preview

A: Product rule is: (uv)'=u'v+uv' Here u=2x+1 and v=2x+3 So, u'=2 and v'=2  

Q: Please solve

A: Acoording to the problem Salt = 30pound in 600 gallons of Salt water =3.595 gallon Which mean - 3.59...

Q: Multivariate Calculus Partially differentiate the following equations with respect to x1 and x2. No...

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Q: Find  y(t) using Laplace transform.

A: Consider the given differential equation: Here the objective is to find the solution to a given dif...

Q: 19-22 - Sketching Vectors Sketch the given vector with initial point (4, 3), and find the terminal p...

A: The given initial point is (4,3). a) u=<2,4>We have to find the terminal pointA vector can be ...

Q: Prove that lim x 2 = 4. x→ 2

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Q: If necessary, use two or more substitutionsto find the following integrals.

A:               The given integration is I=∫0π2cosθsinθcos2θ+16 dθI=∫0π2cosθsinθcos2θ+16dθsubstitute u...

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.