Solve the differential equation dy dx Give an implicit solution and use c as the constant. - y = e²y²

Q: find f+g, f-g, fg and f/g and their domains f(x)= 5-x and g(x)=x^2-4x domain of (f+g)(x) in interval…

A: Given:- fx=5-x , gx=x2-4x

Q: Given f(x, y) = y ln(5x – 4y), find fz(x, y) = fy(x, y) =

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Q: x³ + k kx - 23 if x ≤ 3 if x > 3 Determine the value of k that will make f(x) continuous everywhere.…

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Q: 49. Find an equation of the line tangent to the graph of y = √x/(x + 1) at (a) x = 1; (b) x = 1.

A: We need to find equation of tangent.

Q: Use the graph of the function f given below to answer the questions. List the values of x at which f…

A: Given problem:-

Q: Evaluate this

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Q: 0 ryz -y (2x - 3y) dx dy

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Q: Find the indicated limit. x5 +4 lim x→1 5x5 + 5

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Q: Find the derivative of the function using the definition of derivative. f(x) = x³ − 3x + 7 f'(x) =…

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Q: Determine the value of k such that y=4r²-3e2r is a solution to x(1-x)y"'+ (2x² − 1) y' + k (2x − 1)…

A: I am attaching image so that you understand each and every step.

Q: (a) Find the slope of the curve y=x³-7x at the given point P(1,-6) by finding the limiting value of…

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Q: For the function, find the following. f(x) = 8 + 7x + (a) f'(x) (b) f(x) (c) F"(x) (d) f(4)(x) + + 5…

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Q: For

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Q: 1. Verify if y = xe* is a solution of y" 2y + y = 0

A: As per the rules of the company we can answer only the first question and rest others can be…

Q: The strength of a patient's reaction to a dose of x milligrams of a certain drug is R(x) = 8x√/16…

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Q: A cold drink is poured out at 55°F. After 2 minutes of sitting in a 60°F room, its temperature has…

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Q: g(x) = 3 √√x+1

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Q: Given f(x)=2x-4 and g(x) = ax² + 2x-10. If f(g(2)] is four times of ƒ(4), find a.

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Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) 1m (7x²-3x) lim X-0

A: The limit is given by limx→07x2-8xx To evaluate: The value of the limit.

Q: Solve the first-order differential equations using an appropriate method. Find a general implicit…

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Q: The height of a projectile launched into the air is given by f(t)= - 16t2 +97t+9, where t is the…

A: Topic- Average rate of range of function over interval we are given f(t)=-16t2+97t+9Average rate of…

Q: 2. Let a = -784° a. Find an angle coterminal to a such that 0≤ 0 < 360° b. Find the reference angle…

A: To find out the coterminal angle.

Q: 3 How fast does the water level drop when a Cylindrical tank of radius 6 feet drained at the rate of…

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Q: Find the DE by eleminating the arbitrary constants y = C1e^x + C2cos(x) + C3sin(x)

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Q: Find the average rate of change of f(x) = 3x² + 2 over each of the following intervals. (a) From 3…

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Q: Find the general solution of each differential equation. x' X = t² + tx+x² 2t² + tx

A: Given x'=t2+tx+x22t2+tx

Q: F(x)= 3x2+2x-1

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Q: 2. On your own, make a diagram that shows the relationship of the number system which are as…

A: A natural number is a counting number. It starts from 1 onwards. They are located at the right side…

Q: Sketch a graph of the function f(x) = 6 5 4 32 3 2 1 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 -2 -3 -4 3 sin 1…

A: Topic = Graph

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) 9-x² lim x3 3x² + x³ 3

A: Please refer to the image below

Q: 5. 4-3/x lim X→→++* 2+5/x 6. lim 811 2/x-1/x² +5/x³ 4-1/x³

A: We know that 1/infinity tends to 0

Q: Form a polynomial whose real zeros and degree are given. Zeros: 2,1,3,5; degree: 4 Type a polynomial…

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Q: lim f(x) = 9 X→ 1 lim g(x) = -5 X→ 1 lim_h(x) = 0, X→ 1

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Q: F"(x) = f(x) = 36 √√x

A: Given that , fx=36x3 find f''x=?

Q: The limit represents the derivative of some function f at some number a. State such an f and a. lim…

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Q: Find the volume of the solid that results from rotating the region bounded by the graphs of y = y =…

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Q: Verify if y = x4 is a solution of dy/dx = 4y/x.

A: The answer is given below:

Q: separation of variables to find the solutions to the differential equations in Problems 1-12, ect to…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Integrate both sides of this equation. 015 -=[ye-41] = (4t+5) e-4t e-41 = S(4t+5) e-4¹dt ye -4t. =…

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Q: 1 1.) An = (1 + n)ñ

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Q: EXERCISES Determine the equations of the vertical and horizontal asymptotes, if any, of each…

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Q: 2. 2 구 1 (x-4)2, (y+5) 10 (1+5)-1 구

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Q: Given the function f(x) a) Calculate the slope of the tangent line at the point (-2,- 12). = 4x x²,…

A: Here, the given function is: f(x)=4x-x2⇒f'(x)=ddx(f(x))             =ddx(4x-x2)…

Q: Form a polynomial whose zeros and degree are given. Zeros: 2, 2, 6; degree: 3 Type a polynomial with…

A: Given query is to find the polynomial.

Q: ven that (b) lim [g(x)]³ lim f(x) = 4 x-2 find each limit, if it exists. (If an answer does not…

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Q: lim g(y) where, g (y) = Jy²+5 13-3y lim g (y) y² +5 ify -2 ify <-2 if y2-2 9 (3) = -1.9 DNE y²+5 if…

A: The given function is a piecewise function represented as: g(y)=y2+5   if y&lt;-23-3y   if y≥-2

Q: Can calculus limits have a decimal form?

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Q: N 1. Solve each of the following initial value problems and plot he solutions for several values of…

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Q: Determine the x coordinate of the inflection point for the graph of h(x) = x³ 3x² +9x+8. -

A: Given, h(x)=x3-3x2+9x+8

Q: The national debt of a South American country t years from now is predicted to be D(t) = 85 + 9t4/3…

A: This is a problem related to derivative and function calculation. Please follow the procedure given…