Solve the following differential equations. Question 6 ( 3x – 1 ) y’ = 6y - 10(3x – 1)1/3

Q: Consider the equation y" - 36y = 6 cos (6t) + 6 + e6t. According to the method of Undetermined…

A: Please see the below picture for detailed solution.

Q: F(x) = psolute min solute max +25 on [-7,7] 11

A: Topic:- application of derivatives

Q: 36. y = 4x² , A costant

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Q: Suppose a company has fixed costs of $33,600 and variable cost per unit of x + 222 dollars, where x…

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Q: Provide an appropriate response. 7) Find the derivative of the function f(x) = A) 16 B) 17 2x - 7 3x…

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Q: a. In 25-In 64 +In 27 3

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the maximum and minimum values of the function f(x, y) = e subject to a³ + y³ = 16 Please show…

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Q: 9. y = ln *³(x-¹)(use properties of logarithms) (x+1)4

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Q: y = p02-0

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Q: 6) Daniel throws a baseball from the outfield to home plate. The height, h, in metres, of the ball…

A: Since you have posted  multipart question, I can do first three sub parts as per our company…

Q: 19. The graph of f is shown to the right. For which value of x is f'(x) the smallest? [A] x=6 [B]…

A: given graph of f(x)

Q: Given that Vƒ(2, −11) = 6 i – 3j, find the directional derivative of the function ƒ at the point…

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Q: What is a piecewise-defined function? Give examples

A: A piecewise function is a combination of different functions along with different values of the…

Q: Find the limit lim h+0 f(−11+ h) − f(−11) h ‚ if f(x) = √1069 – 6x².

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Q: 1. 3 A certain fraction has the value. If its 4 numerator is decreased by 7 and its denominator…

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Q: What is a periodic function? Give examples. What are the periodsof the six basic trigonometric…

A: Function: In mathematics, a function is an expression, rule, or law that establishes the…

Q: 2. y = ln 3. y = 1+sinx 1–sinx e3x-e-3x e3x+e-3x (use properties of logarithms)

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Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

A: Given query is to find the value of the integral.

Q: 4x² 1. Let y=f(x) = 4x+1

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Q: Use the intermediate value theorem to show that the polynomial has a real zero between the given…

A: Given function:- fx=x3-5x+8

Q: Consider the initial value problem (*) ty" + (2t + 6) y' + (t + 6) and_y'(1) = 2 8 |y(1) = - e Given…

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Q: If ƒ and g are real-valued functions, how are the domains ofƒ + g, ƒ - g, ƒg, and ƒ/g related to the…

A: Let f and g be functions with domains A and B. To find the domains of the following: f+g, f-g, fg,…

Q: Find the extreme values of g(x, y) = x² + y² + x²y on the circle x² + y² = 12 using the method of…

A: To find the extreme values of  g(x,y)=x2+y2+x2y...(1) on the circle f(x,y)=x2+y2-12=0...(2)

Q: In Exercises  use graphing software to determine which of thegiven viewing windows displays the most…

A: The function given is as follows: fx=5+12x-x3 Rearrange the above function: fx=-x3+12x+5

Q: A tank contains 2240 L of pure water. A solution that contains 0.07 kg of sugar per liter enters a…

A: Given initial amount of water in tank is v(0) = 2240 L Let v is volume in L, x is amount of sugar in…

Q: Sind f(x) (8x-91-4 Sind derivative ہا۔

A: To find derivative of given function.

Q: J + tan x)² sec x dx

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Q: Evaluate the integral: 0x = 10 tan (0) 10 sec (0) 100 sec (0) (A) Which trig substitution is correct…

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Q: Solve the ff. first order DE using Separation of Variables 2 b. x²dx + y(x − 1)dy = 0

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Q: Pythagorean Problems Calculate the distance between points x and y. Give your answer to 1 decimal…

A: To calculate the distance between x and y.

Q: The radius r of a sphere is increasing at a rate of 4 inches per minute. (a) Find the rate of change…

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Q: Consider the function f(x) = S|1-x²| cos(x) x ≤ 0 x>0 (a) Evaluate the function at x=2. Enter your…

A: The given function fx=1-x2x≤0cosπ2xx>0 We have to sketch the graph of the function and find the…

Q: 22. Find lim h-0 f(x+h)-f(x) h f(x) = 5x-4, x=6 The lim f(x+h)-f(x) h for the given function and…

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Q: Finding the Maximum or Minimum Value of a Quadratic FunctionDetermine whether the quadratic…

A: A quadratic function has a maximum value if it's second derivative has a negative valueand  the…

Q: Which of the following limits represents a derivative of the function f(x)=√x- ? O 1 lim h 0…

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Q: 12. lim n→∞ n πί Σ[cos (+) + sec² (+)1 COS 3n i=1 TT 3n

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Q: Find the derivatives a) f(x)=√x+1 b) f(x)=sin(x+3) at a=0 c) f(x) = == X x+1 of the following…

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Q: Find (without using a calculator) the absolute extreme values of the function on the given interval.…

A: To find absolute extrema of the given function

Q: Identify the open interval(s) where f is concave up. [A] (-∞, -1) [B] (-∞, -3) U (-1,2) [C] (-1,00)…

A: for concave up , f'(x) is increasing For given graph , f'(x) is increasing on

Q: A thermometer is taken from a room where the temperature is 23°C to the outdoors, where the…

A: Explained below

Q: A point is moving along the graph of the given function such that dx/dt is 2 centimeters per second.…

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Q: 1. Let y=f(x)= 4x² 4x + 1

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Q: Find the average rate of change of the function over the given interval. R(0) = √30+1; [1,8] AR ΔΘ…

A: The average rate of change of the function Rθ over the interval a, b is given by ∆R∆θ = Rb-Rab-a.

Q: Evaluate the limit of the function as x approaches zero from the left (0): lim, 0- 00 01 O None of…

A: To evaluate: limx→0- -sin(2x)1-cosx ⇒limx→0- -sin(2x)1-cosx = limx→0- -2sinxcosxsin2x1+cosx⇒limx→0-…

Q: A line has the equation  y = 9x + 1. (a) This line has slope  ?. (b) Any line parallel to this…

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Q: Initial condition. 14. Differential equation: Initial condition: dr dt r(0) = i + j = (t³ + 4t)i +…

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Q: Determine whether or not the graph represents a function. Be prepared to justify your answer using…

A: The graph is To determine: Whether the graph represents a functor or not.

Q: Sinc In (x+15) dx Choose the correct answer below. OA. (x+15)+ In (x + 15) + C Oc. (x+15) In (x+15)…

A: Given, Evaluate: ∫ln(x+15)dx

Q: Evaluate the integral: (A) Which trig substitution 36 sec (0) X = X = 6 sec (0) X = 6 sin(0) ○x = 36…

A: The given integral is  ∫36-x24x2dx

Q: In Exercise use graphing software to determine which of thegiven viewing windows displays the most…

A: Given, fx=x4-7x2+6x