differential equation is given along with the field or problem area in which it arises. Classify it as an ordinary differential equation (ODE) or a partial differential equation (PDE), give the order, and indicate the independent and ependent variables. If the equation is an ordinary differential equation, indicate whether the equation is linear or nonlinear. 1+ =C, where C is a constant (brachistochrone problem, calculus of variations) Classify the given differential equation. Choose the correct answer below. linear ordinary differential equation nonlinear ordinary differential equation O partial differential equation The order of the differential equation is (Type a whole number.) Vand the dependent

Q: Finance. Suppose that $7,500 is invested at 5.7% annual interest rate, compounded monthly. How much ...

A: Investment is (P)= $7,500  Interest (r)= 5.7% = 0.057  n= 12 find amount in  A) 6 months , B) in 7 y...

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Q: Select the function that is even. f(x) = 2cos(x) f(x) = 2cot(x) f(x) = 2sin(x) f(x) = 2tan(x)

A:

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A: The given function f(x)=lnx lnx2 lnx3

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A:

Q: Parabolic Two-way Tunnel Dimensions of the Tunnel: 18 feet by 38 feet Find the standard form and g...

A: NOTE: Refresh your page if you can't see any equations. . the equation of a parabola is given by as...

Q: f(x) = (0.75)-2x+2 + 6

A: For the given function

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A: According to question,Given function.fx = ex2

Q: Estimate the slope of the tangent line to the curve at the given point (-4.5,4.911) on the graph to ...

A: The given point is: -4.5, 4.911   Estimate the slope of the tangent at the given point.

Q: use a table to estimate the limit of g(x)= sin2x/3x as x approaches zero. show how to plug in calcul...

A:

Q: Choose the correct graph of F(x) = 2 sin(2x + T): 2 1 27. 3 -1 -2

A: Find your answer below 

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Q: Let lim f(x)= 11 and lim g(x)=9. Use the limit rules to find the following limit. X-9 lim [f(x)- g(x...

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Q: Direction: Find the derivative of the function. y = -z² + 3 Select one: O y' = -2x O y' = 2x O y' = ...

A:

Q: 6. a. Show that the vector á of b = (3, 1, 4) and ở = (1, 2, –3). (1, 12, –29) can be written as a l...

A: We have to write the vector in the linear combination of two vectors 

Q: Find the exact value of s in the given interval that has the given circular function value. V3 CoS s...

A: Topic = trigonometry

Q: 11) Find the slope of the tangent lines on the curve y = 6x³ + 24x² – 39x – 43 at points .- ) 478 (-...

A: As you have asked multiple questions so I have answered first question as per the guidelines.

Q: e2x dx 4 + e4x 13.

A: We have to find the integral of the given function. 

Q: +x² xp

A: We will evaluate the given integral as shown below

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), E (0,4,0), and (0,0,2)

A: The vertices of the tetrahedron are (0,0,0),(1,0,0),(0,4,0),(0,0,2).  x varies from x:0→1y varies fr...

Q: Let f(x) = 7 9(z) = and 2 7 7x - h(x) : | (a) Find the domain of g. Write your answer in interval no...

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Q: The region bounded by f(r) la + 6x + 16, r = 0, and y =0 is rotated about the y-axis. Find the volum...

A: solution:-the region bounded byf(x)=-x2+6x+16, x=0 and y=0rotating about the y-axisusing cylindrical...

Q: x2 dx 25 - x2

A: Here we use the trigonometric subsitution method to solve the given Integral.

Q: The value of tan is -1 1 undefined

A:

Q: 6. a. Show that the vector à = (1, 12, –29) can be written as a linear combination of b = (3, 1, 4) ...

A: Here we have to show that the vector a=(1,12,-29) can be written as a linear combination of b=(3,1,4...

Q: #37

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Q: ずx 1

A:

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Q: Complete the square: 2? + 3z+ = (x+ 22 – 5x+ = (r- = (x+ %3D

A: Given that:                                

Q: dy If y = (t + 2t + 5) (7Ł² + 3), find dt dy dt

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Q: f(x) = E g(x) = x2 - 3x Find (fo g)(x). Find the domain of (fo g)(x). (Enter your answer using inter...

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Q: 2x+4

A: Topic = Integration

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A: Given that a man drops a penny from the top of a 500 m tall building. After t seconds it has fallen ...

Q: Direction: Find the derivative of the function. y = 2e* +e* Select one: O y' = 3 – 2e* O y' = 3e + 2...

A: We know that; The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1 Given: y=2e-x+e3x

Q: Rewrite the following expression in terms of exponentials and simplify the result. (cosh 3x + sinh 3...

A:

Q: Calculate the work W against gravity required to build a cylindrical column of height 6 m and radius...

A: Formula: Weight = mass×gravity ×hight  

Q: Find the value x=a where the function is discontinuous. For the point of discontinuity, give (a) f(a...

A: Given the query is to find the point of discontinuity and find indicated limits.

Q: Use the method of cylindrical shells to find the volume of the solid formed by revolving the region ...

A:

Q: 12) A right circular cone has a fixed height of 7 units. Find the rate of change of its volume V wit...

A: NOTE: Refresh your page if you can't see any equations. . the volume of the right circular cone is g...

Q: 68. Let Jr dx. %3D (a) Show that J1 = -e-x²/2. (b) Prove that Jn = -x"-le-x*/2 + (n – 1)Jn–2. %3D (c...

A: Solution is given below:

Q: For problems # 16 £17 to Find the requested derivative Use implicit differentiation ln (x y) x +9 fi...

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Q: Evaluate the integral. In 2 2 e sinh 0 d0 - In 10

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Q: In two or more complete sentences, explain how to find the time it takes for a rocket following the ...

A: We will find the time taken by the rocket to hits the ground as shown below

Q: Suppose that R is the finite region bounded by f(x) = VT and g(z) 4 Find the exact value of the volu...

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Q: 15) Consider the following equations of quadric surfaces: a) x=+-4 b) x? - y? + z? = 4 i) Identify t...

A: 15) b) The given equation is: x2-y2+z2=4...(1)

Q: Given g(æ)+ x/g(x) + 8 = x² + 1, g'(0)=

A:

Q: 4. Determine the constant m such that f(x) = {x2 + m, if x ≥ 3                                      ...

A: Given that: f(x)=x2+m, if x≥32x-m, if x<3

Q: Find the derivative of the inverse trig functions. a) y = cos-1 5x b) y = x· arctan x

A: We can solve both the question as below.

Q: For the piecewise-defined function f whose graph is shown, find the following. (If an answer does no...

A: