Exercise 1 Find the differential equations of the following by eliminating the arbitrary constants: a.) y = x² + Cx b.) lny = C₁x + C₂e¯x c.) y = Ax² + Bx + C

Q: sin cos 0 cos sin

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Q: Evaluate lim (√9x² V92 _5 +1+ 5x+1+3x). - x418

A: Find limit of function

Q: Evaluate each limit, if it exists: x²-4 a)lim 22-4 X-2 1-x² b)lim x-1 1-x x²-4x x-0 x(x-1) c) lim

A: Here we have to find the limit of the functions.

Q: In a Northwest Washington County, the speeding fines are determined by the formula: F(s) 15(855) +…

A: F(s)=15(s-55)+80

Q: : Fit a second order polynomials to the data in the following: 5 6 12 13 X Y 1 4 3 8 4 10 7 10 8 co…

A: From given data

Q: If f(x) ƒ'(x) = | = 4x sin cos x, find Find f '(1) =

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Q: Given that f(x) = x² - 7x and g(x) = x + 8, find: a) (f+g)(-1): b) (fg)(1) c) (fg)(-1) = (-/-) ( −…

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Q: Solve the problem. The population P of elephants in a wild animal preserve changes with time (in…

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Q: 1. For the function y = 5x³ - 4x a. Determine the average rate of change between x₁=3 and x₂ = 5. b.…

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Q: Find a and b so that f(x) = 2x+1 + ax² + bx+ 2021 satisfies the following: ● ● The average rate of…

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Q: what if x approaches the negative infinity?

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Q: Evaluate each limit, if it exists: a)lim ²-4 X-2

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Q: Find k so that the function f(x)= 2x+5 if x ≤2 kx +1 if x > 2 can be defined so that it will be a…

A: Given function, f(x)=2x+5               if x≤2kx+1                if x>2

Q: 15. d e f 9 h i a b C 'a b с de f =-6 g hi

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Q: Given f (x) below, select ALL of the true statements. lim, 4+ f(x) = 1 lim-4 f (x) = 1 lim, 4- f (x)…

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Q: Evaluate lim 1 1-2x X-3 x-3

A: Here we have to use the concept of limits

Q: B: Fit a second order polynomials to the data in the following: X Y 1 4 3 8 4 10 5 12 6 13 10 69 8…

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Q: If f(x) ƒ'(x) = ƒ'(4) = = 4 sinx + 4 cos x, then

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Q: Find the solution of the differential equation dx 2y +x+ xy3

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Q: 9. y = (1 + x²) Arctan x 10. y = sin(Arccos x)

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Q: Find the solution of the differential equation (x + 3y)dx − xdy = 0. a. 2y - x = Cx³ b. 2y + x = Cx³…

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Q: The limit represents a derivative f'(a). Find ƒ and a. sin (+h)-/ h lim h-0 (Express numbers in…

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Q: B) Find the area of the region between the curves x = quardrant. = y² and x = y + 2 in the first

A: The given curves are x=y2 and x=y+2.   Now find the points of intersection between the given curve.…

Q: Urgent!

A: Given statement is as px:x2≥1

Q: A certain retailers will buy 22 cordless phones from a supplier if the price is $72 each but only 35…

A: This question can be solved by applying the concept of linear equation.

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 9ti −…

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Q: The condition is, H (7) = 17.9; 260 1+ Ce-0.004 (7) 17.9= ⇒1+C₂-0.004(7) ⇒Ce-0.004(7) 260 17.9 -662)…

A: a differential equation is an equation with one or more derivatives of a function. The derivative of…

Q: . The population of Bougainville exponential function P(t) = ae use it to calculate when the…

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Q: dz dt If (z=x. y), where x = cos (t) and y = sin (t) 03. Use the chain rule method to find

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Q: 6. Sketch and label the graph of a function that describes the given situation. Pick variables for…

A: a. In this case, the population size of warthogs cannot go above 512 warthogs, so, the given…

Q: Q2. Determine the complete solution for the following differential equation: y"+y+0.25y=0 if y(x) =…

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Q: If f(x) 4x + 2 3x + 3 find:

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Q: Consider the equation x + 2a of the given equation? O O x= O x= P= 5a b 4 11a-b 4 b-11a 4 b-5a 4…

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Q: 65-4 52-45+16 4/ A: 1- L-1,

A: given the function in laplace form

Q: Use transformations of the standard cubic function f(x)=x3, to graph the following function…

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Q: If f(x) = ƒ'(x) = 4x(sin cosx), find

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Q: Determine f'(a) for a = 2.5, 4, 7. 5 4 3 2 1 y 1 234 567 89

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Q: 7. S X e dx - X et + 4e¯x

A: As we know from the exponent rule: xaxb=xa-b And the common integral is: ∫1ax+bdx=1alnax+b+C   The…

Q: Solve the given linear differential equation. Use C as the constant of integration in your solution.…

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Q: 9.  Use Simpson's rule with  n = 4  equal subintervals to approximate the following. (Round your…

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Q: Given f (x) below, select ALL of the true statements. lim-4+ f (x) = 1 lim, 4 f (x) = 1 lim,-4-f(x)…

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Q: 4x−³+2 3 8. S ² X - 2 - X dx

A: Given :∫4x-3+2x-2-xdx

Q: Find values of cl and c2 so that the given functions will satisfy the prescribed initial conditions.…

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Q: 4 1 82

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Q: B: Evaluate the following: 2- 6 I (5.66) 5r (0.66)

A: Given 6Γ5.665Γ0.66

Q: Consider the graph of  (10 − x)y2 = x3. Find the slope of the graph at the given point.

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Q: 3y(x²-1)dx + (x³ + 8y - 3x)dy = 0; when x = 0, y = 1.

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Q: The count in a bacteria culture was 100 after 20 minutes and 1600 after 35 minutes. Assuming the…

A: The growth of bacteria is given as , ft=cekt Growth rate (k)=?

Q: b. y = 2x² - 1 x + 1

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Q: Given that f(x) = 6 -√²+1 and g(x) = x - 7, find: 2 a) (fog)(-2) b) (fog)(x) = 6-√(x-7)²+1

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