Let f(x) be the function 9 x² − 3 x + 4. Then the quotient a = Number and b = Number f(4+h)-f(4) h can be simplified to ah + b for:

Q: Consider the function f(x) = 3x²-5x+2. Use it to find f(4), f(-1), and f(a + 3). f(4) = 30 O…

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Q: Evaluate the following integral. S= 2 x³√x² - 1 dx =

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Q: Solve for the value of C in the equation: (2xy¹ey + 2xy³ + y)dx + (x²y4e¥ − x²y² – 3x)dy = 0 when…

A: The given equation is; (2xy4ey+2xy3+y)dx +( x2y4ey - x2y2-3x)dy=0 y(1)=1.

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Q: The population of the world was about 5.3 billion in 1990. Birth rates in the 1990s ranged from 35…

A: Here assume P(t) be the population of world in billions at any time t in years

Q: Suppose Use this to compute the following limit. Limit= Number What Theorem did you use to arrive at…

A: Snadwich TheoremSqueeze Theorem:  If g(x)≤f(x)≤h(x)  for all x in an interval containing a point…

Q: 2 5. Sketch the region bounded by the curve x 2 = y and the line x = y + 2 and find the volume of…

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Q: Use the Lagrange multipliers to find the maximum and minimum values of f(x, y) = 2x + y - 2z subject…

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Q: Solve for the value of C in the equation: +ycotx OA. -5 O B. 5 C.-4 O D. 4 dy dx E. None of the…

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Q: Another model for a growth function for a limited population is given by the Gompertz function,…

A: The givne growth function for the limited population is dpdt=clnkpp…

Q: If ƒ(1) = 5, must lim x approaches 1 ƒ(x) exist? If it does, then must lim x approaches 1 ƒ(x) = 5?…

A: Given :-f(1)=5Now, we have to find that limx→1f(x) exists or not.And if  limx→1f(x) exists then…

Q: Sorry forgot to specify, find the zeros

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Q: 3. Consider the initial value problem y′ +y=1-², y(0) = 30› where yo denotes some real constant. (a)…

A: To find the solution of given differential equation.

Q: The integrating factor (IF) of the equation: (2x³y² + 4x²y + 2xy² + xy + 2y)dx + (2y³ + 2x²y + 2x)dy…

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Q: True or False The slope of a nonvertical line is the averagerate of change of the linear function.

A: The average rate of change of the linear function is the slope of a nonvertical line.

Q: Find the explicit solution of dy/dx=2xy² + 3x²y², y ( 1) = − 1 O 1/y=3-x²-x3 Oy=x²/2+x²³/3-3…

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Q: (g) Differentiate g(x) = /1-². cos¹ (√) 3

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Q: 15. Find the limit. lim X48 lim X-8 sin 15x 19x sin 15x 19x =

A: See this solution in below.

Q: 13. Suppose that lim f(x) = 13 and lim g(x) = -7. Find the following limits. X-4 X-4 a. lim…

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Q: The domain of f(x) is all real numbers except x - 3 x + 5 f(x) = Blank 1:

A: The objective of the question is determine the domain of the given function.

Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) E.…

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Q: Find the directional derivative off at P in the direction of a. ƒ(x, y) = 5x²y³; P(2, 2); a = 3 i −…

A: This question can be solved using the concept of partial derivatives and vectors.

Q: Problem 1. Is the following true or false? Justify your choice. 4x (x − 1)(x + 3)' Bx + C x + 3 To…

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Q: Uranium-238 (U-238) has a half-life of 4.5 billion years Geologists find a rock containing a mixture…

A: Half life = 4.5 billion years N(t)=0.77* N0t= ?t12=4.5 billion years

Q: Obtain the differential equation whose general solution is y = C₁ + c₂e³x. 3x O A. O B. C. D. O E.…

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Q: Which of the function is not an exact equation of the first order? A. (e³ + ycosx)dx + (xe³ + sinx +…

A: We have to find which of the following function is not exact. We

Q: What is the standard form of this linear equation in one variable: (y + 1)dx + (4x − y)dy = 0? |…

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Q: Solve for the value of C in the equation: O A. 1 OB. 2 O C.3 O D. 4 E. None of the Choices dy dx…

A: Find integrating factor of linear differential equation

Q: In problems 11-12, express each limit as a definite integral. (they are given using right endpoints)…

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Q: What is the standard form of this linear equation in one variable: (y + 1)dx + (4x − y)dy = 0? None…

A: Given (y+1)dx+(4x-y)dy=0 Multiply both sides by 1(y+1)dy (y+1)dx(y+1)dy+(4x-y)dy(y+1)dy=0…

Q: Solve equation log5x+log(x-1) = 2 without using a calculator.

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Q: Which of the following statement is TRUE? 8:01 AM A. An ordinary differential equation (ODE)…

A: keeping a note ?as per our company guidelines we are supposed to answer ?️only first 3 sub-parts.…

Q: A chemical substance has a decay rate of 6.5% per day. The rate of change of an amount N of the…

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Q: What is a suitable integrating factor that can be used to solve the equation dy dx A. e B. 3 ex D.…

A: To find Integrating Factor.

Q: Find the general form of f if f'(x) = 10f(x).

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Q: A community skating rink is in the shape of a rectangle withsemicircles attached at the ends. The…

A: Given data, The length of the rectangle given is 20 ft less than twice the width. The thickness of…

Q: Find the exact length of the curve. y=ex, 0≤x≤ 3

A: Length of curve =∫ab1+dydx2dx

Q: 1) Determine whether or not the following equations are exact

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Q: Which of the following equations is NOT an exact equation? | OA. (2x sin y + y)dx + (x² cos y + x)dy…

A: Exact differential equation A first order differential equation M(x,y)dx+N(x,y)dy=0 is called an…

Q: the cable of a suspension bridge hangs in the form of a parabola. the distance between two towers is…

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Q: 01

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Q: The rate of change of the variable y in terms of another variable t is equal to the expression 5t4 -…

A: Your option is incorrect or may be last option correct . But my solution is correct .

Q: Graph the functions in Exercises .37. y = sqrt(x + 4)         38. y = sqrt(9 - x)

A: Given data:- 37. y=sqrt(x + 4) 38. y=sqrt(9-x)

Q: The figure shows the positions of an object as a function of time t. S 10 J540 501 + 20 30 40 50 t…

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Q: 2. Use the graph below to determine whether the statements about the function y = f(x) are true or…

A: NOTE: Refresh your page if you can't see any equations. . as we can see from the graph, the…

Q: Which of the following is NOT true about the linearity of differential equations? O A. Which of the…

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Q: Find the total area bounded by the graphs of f(x) = 3x³ - x² - 10x and g(x) = -x²+2x. 32 units² O 8…

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Q: Which of the following statement is TRUE? O A. An ordinary differential equation (ODE) contains…

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Q: Find the directional derivative of f at P in the direction of a. f(x, y) = 13 tan (²); P(-14,14);…

A: The given function is fx,y=13tan-1yx. To find the directional derivative, find the gradient of f.…

Q: Which of the following is a non-homogeneous function? O O tan³y/x | xLnx − xlny x³ - xy + y² (y² +…

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