How to know if an equation is a solution to a first order differential equation? Please give clear explanation because I am totally confused! Use the image below as an example to explain the question.

Q: Indicate whether the following equations are true or false for all integrable functions f. a) b) c)…

A: a) We know that properties of integration,…

Q: Evaluate the indefinite integral [sin³ sint cos³ tdt =

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Q: 2. Circle the function if it is exponential, or if it is a transformation of an exponential…

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Q: 3) Use the appropriate integral formula for the length of a curve represented by a function y = f(x)…

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Q: Q2: Use the substitution x² = sing to show that 1 √ √ ² x dx = [] 4√2TE

A: See this solution in below.

Q: 12x-8y+11=0

A: We have to choose the correct option from the given options accordingly to the given information

Q: What is the center (h,k) and radius of the cirlce: x2+y2-6x+4y=12

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Q: v = fb an V (x − 3)(x x= y₁²³-4y+3 чуте x = 3 X b 2₁₁ × [ f(x)] dx 29 x= 1x 2 y

A: v=2π∫13y(1+(y-2)2dy v=2π∫13y(1+y2-4y+4)dyv=2π∫13(y+y3-4y2+4y)dy

Q: 1-sine 8-π/2 1+cos20 3) lim

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Q: Say if it’s FUNCTION or NOT. Answer those 5

A: We need to determine given graphs are functions or not.

Q: The position function of a particle is given by r(t) = (4t², 3t, t²- 8t). At what time is the speed…

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Q: 31. ผ n=1 √n + 3 n2 + 17

A: We need to find out the convergence of the series by the use of limit comparison test.

Q: Consider the function (for question G) S(x) ax³ bx³ + k G. What will happen to lim S(x) if a, b, and…

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Q: 3. Check for homogeneity and obtain the general solution. (Let y=vx and 2C=C) dy x-y dx x+y

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Q: Let F(x, y) = 1 + √√1 − y². 1. Evaluate F(3, 1). Answer: F(3, 1) = 1 2. What is the range of F(x,…

A: Let's solve for function value at given point and its range.

Q: 37. Σ n=1 1 3η τη

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Q: If ƒ and g are continuous functions with ƒ(5) = 2 and, lim[2ƒ(x) − g(x)] = 5 find g(5)

A: Given:- limx→52fx-gx=5 and f5=2if f and g are continuous functions then need to find g5

Q: " + 4y = cos 3x

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Q: Check whether each differential equation has the indicated solution. Determine which solutions are…

A: Here is the ordinary differential equation. As it is a homogeneous equation first we let   V = emt…

Q: 10.) Find the simplified form of the difference quotient. f(x)=x² + x

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Q: if x ≤ 1 if r> 1 Calculate the following limits. Enter "DNE" if the limit does not exist. f(x) = Let…

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Q: 1) Let f(x) Choose the best answer. = sin² (3x4). Derive the derivative f'(x).

A: The explanation of answer as follows

Q: Solve (e) (1-x²)y' = 4y; y(0) = 1.

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Q: Find the tangential component of acceleration for a moving particle if its position function is r(t)…

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Q: x that makes each statement true. 15. 3 - 2 -X 4 = - 9 16. y². y² =

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Q: 20-25 -**- Solve (px - y) (py + x) = 2

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Q: Q3/ Use the l'Hopital's rule to find the limits x-8x² x→∞ 12x²+5x 2) lim

A: The limit is given by limx→∞x-8x212x2+5x To evaluate: The value of the limit using L'Hopital's rule.

Q: ph are given. y 2 -4 -6 2 4 X

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Q: True or false? If lim(xn) = x and lim(yn) = y and for all n, xn < yn, then x < y.

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Q: I--2+ b. lim (x+3) --2 2+2 |z+21 2+2 5 2+0+ cos 2-1/ b. lim cos z-1 2-0 cos 2-1/

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Q: (2p+3; p1 Given: f(p) = 2 7-2p Evaluate lim f(p). p-1-

A: Given: fp=2p+3 ; p&lt;12 ; p=17-2p ; p&gt;1   From the given piece-wise function, when p approaches…

Q: Let U be the universal set of natural numbers less than 11. Consider the following two sets. A = {7,…

A: NOTE: Refresh your page if you can't see any equations. . U be the universal set of natural…

Q: (d) d dy 11 = 4- 2x cos y 3y² tan 2x - - 2y3 sec 2x 2 sin y

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Q: 1 A used piece of rental equipment has 5 years of useful life remaining. When rented, the equipment…

A: A piece of rental equipment has 5.4 years of life remaining When rented,the equipment brings in $600…

Q: Let U be the universal set of natural numbers less than 11. Consider the following two sets. A = {6,…

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Q: The adul dicts that the adult population of the town will increase by 4% each year, ming a geometric…

A: At the end of one year population = 20000 increased by 4%  a. Population at the end of 2nd year

Q: Evaluate: [4 dx/(x²-4). A. In (x-2)(x + 2) + C C. 2 arc tan x/2 + C B. In (x + 2)/(x-2) + C D. 4 arc…

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Q: f(x)=5sin(2x) - 2x² - 4x Find the maximum or the minimum of the function using newton's method of…

A: Newton's method of optimization is the general method for finding the minima or maxima of the given…

Q: The two vectors a and b in the figure have equal magnitudes of 10.9 m and the angles are 0₁ = 34°…

A: Shift the given vector b and then do the vector sum after breaking the components.

Q: Solve dy dr 3y-1x Er

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Q: 5. y = sec(In x) 7. y = tan (ln(5x))

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Q: Let f(x, y) = 4√√xy² + 4y+exy. Suppose that z = f(x, y) with x = ln(2s — t²) and y = 2s²t² + t. Use…

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Q: Find the integrals: 1- xdx A. -2/3 (1-x) 3/2 B. 2/3 (1-x)3/2 + C C. -2/3 (1-x)3/2 + C D. -2/3 (1+x)…

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Q: Suppose that a certain car has the following average operating and ownership costs. Average Costs…

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Q: f (x, y)=√x-2+√y-1

A: The objective is to find and and sketch the domain of the function.

Q: plot 1 2√x+y + 1 2√x-y

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Q: 3- 2 01 -8-7-1 T 2 -3- # Determine which one of the following rules for continuity is first violated…

A: from graph f(-1)=-2

Q: Q4. B. Find the tangential vector (T), normal vector (N) and binomial vector (B) for the position…

A: Find tangential, normal component

Q: Suppose that f is continuous on [0, 6] and that the only solutions of the equation f(x) = 3 are x =…

A: f is continuous on [0,6] and that the only solution of the equation f(x)=3 are x=1 and x=5.If f(4)=5…

Q: The daily cost per unit of producing a product by the Ace Company is 35+ 0.2x dollars and the price…

A: To find out the revenue function, cost function, profit function, marginal profit.