Differential equations -Separable dy/dt=3+5y

Q: Use transformations of the standard cubic function, f(x) = x³, to graph the function h(x) = 2x⁰. UL

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Q: Find the average value and the value(s) of c guaranteed by the mean value theorem for integrals if…

A: This theorem states that a continuous function on closed and bounded interval has at least one point…

Q: Consider the graph of the function g(x): -2- 0 2 (a) √ ² g(x) dx = [2 (b) 6 Sº The graph from x = 2…

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Q: f(t)=−5t2−4t+5 Find f′(t):  Find f′(1): Find f′(2):

A: Given that  f(t) = -5t2 -4t +5 We need to find  (1)  f'(t)  (2) f'(1) (3) f'(2)

Q: he area of the segment of a sphere formed by revolving the graph of y = √25-x²,0 ≤ x ≤ 4, about the…

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Q: 3. Let R be the region bounded by the graph of y = 1-² and by the positive coordinate axes. Using…

A: Volume of a solid form by cylindrical shell method is given by V=∫ab2πr(x)f(x)dx     where,   a≤x≤b

Q: Given the vector-valued functions =e=³t+e=³t+ 3tk 3t е (t) v(t) = 5ti − 5t²j + 3k -

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Q: Find the horizontal asymptote, if any, of the graph of the rational function. 16x 2 8x²² +3 f(x) =…

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Q: (a) (b) (c) dy (2x-5)² = dx y dy=3x²(y-1) dx dy_y+2 = dx x+1

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: y = 3x³ + 33x² + 57x Find the critical numbers. (Enter your answers as a comma-separated list. If an…

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Q: Section 4.1 Problems In Problems 1-8, find the derivative at the indicated point from the graph of y…

A: To find derivative of the given function.

Q: n the vector-valued fur = e²t+e-5t + 3 ว = 4ti – 3t²j – 2 3+27 - d dt ū · v) ( − 2) = -(u(t). v(t))…

A: Topic:- application of derivatives

Q: 211. S 3x +4 (x²+4)(3x) -dx

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Q: the family of solution of the equation (x-2y)dx+(2x+y)dy=0.

A: We will find the required.

Q: Why will the solution to dy/dt = y2 grow faster than the solution to dy/dt = y (if we start them…

A: We have to solve 2 questions.

Q: In2-1 , y=0, x= 1, and x = e. 3. Find the area of the region bounded by y= 5x"

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Q: Determine whether the Mean Value theorem can be applied to f on the closed interval [a, b]. (Select…

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Q: Find the unit vector u in the direction of (2, - 2) Give EXACT answer. You do NOT have to simplify…

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Q: If a rock is thrown upward on the planet Mars with a velocity of 15 m/s, its height (in meters)…

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Q: Find the transform of the given function by use of a table. f(t) = 4t³e²t

A: laplace transform of the function f(t)= 4t3e2t

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

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Q: Given the vector-valued functions ū(t) = e5ti + e¯4tj + tk v(t) = − 3ti – 2t²j + 3k

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Q: Let F(x) = f(x³) and G(x) = (f(x))³. You also know that a² = 10, f(a) = 2, f'(a) = 8, ƒ' (a³) = 6…

A: Given that Fx=fx3 and Gx=fx3 The given values a2=10, fa=2, f'a=8, f'a3=6 We have to find the values…

Q: Use cylindrical shells to find the volume of the solid formed by rotating area bounded by the gra…

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Q: Let 7' (t) = ( − 4t³ + 5, t² + 2t¹, − 3t²). Find the line (L) tangent to r(t) at the point (1, 3, 3)…

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Q: cos (3x) - ² (-3sin (3x)) dx

A: Take the integral to be calculated as I1 and then add it to the original integration.

Q: Suppose that the dollar cost of producing x appliances is c(x) = 700+ 110x-0.4x² a. Find the average…

A: We need to find cost.

Q: Part E: Recall that GPA = (total points)/(total credit hours). What is your friend's overall GPA?…

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Q: A B C D v(t) A particle traveling on the x-axis has position r(t) at time t. The graph of the…

A: Here we have to find the total distance traveled by the particle over the given time interval.

Q: Find the first and second derivatives. y = 6x² - 13x - 5x dy dx -0 d²v dx² 4

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Q: (a) Find the average velocity of the object during the first 6 seconds. X m/s -9.8 (b) Use the Mean…

A: Given query is to find average rate of change and apply mean value theorem.

Q: Find the arc length (s) of the curve r(t) = (4t + 2, −5t + 3, 2t - 5) for - 3 ≤ t ≤ 2

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Q: measured in hours. Determine the time intervals when the train is slowing down or speeding up. The…

A: Given query is to find the interval where train is speeding up and down.

Q: 3. Find the characteristic equation for the matrix below and determine its eigenvalues and the…

A: NOTE: Refresh your page if you can't see any equations. . find the matrix A-xI, where x is the…

Q: Determine the x-coordinate(s) of any relative extrema and (1) inflection points of the function y=x…

A: The function is given by y = x2lnx4 To evaluate: The x-coordinate(s) of any relative extrema and…

Q: Evaluate the integral [²(3x² - 2x + 5) d.

A: The given integral is 3x3-2x+5, limit from 0 to 2.

Q: Find y''. y'" y = x(3x+4)4 |||

A: Topic:- derivatives

Q: The displacement from equilibrium of an object in harmonic motion on the end of a spring is 1 y =…

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Q: The function for a current is /(t) = 9cos 120nt where / is the current, in amperes, and t is the…

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Q: Differentiate the square root of x / (1+x

A: Given query is to find the derivative of the function.

Q: A body moves on a coordinate line such that it has a position s= f(t)=12-4t+3 on the interval 0st≤6,…

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Q: Ali will rent a car for the weekend. He can choose one of two plans. The first plan has an initial…

A: Plan first  initial fees = $39.98 and cost on additional per mile driven is= $0.20  Plan second…

Q: Let f(x) = 4x - 32√x and a = 4. Compute f'(x) and find an equation for the tangent line to the graph…

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Q: Use the Chain Rule to calculate the partial derivatives g(x, y) = sin(x² + y²), x=3v- 3u, y = 4u +…

A: By using chain rule to calculate the partial derivatives ∂g∂u, and ∂g∂v.gx, y=sinx2+y2, x=3v-3u,…

Q: 2. Find the equation of the tangent line to the graph of f(x) = x³ - 2x² + 5x -3 at the point (1,1).

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Q: differentiate (square root of x)/(1+x)

A: To find out the derivative of the function.

Q: Find the arc length (s) of the curve (t) = (t – 5, 4t – 5, 5t – 2) for 1 ≤ t ≤ 3 - S =

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Q: The graphs of a = F 3, y = f(x) (solid) and y = g(x) (dashed) are shown; the graph is not drawn to…

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Q: 197. 3x 2 x² + 2x - 8 -dx

A: Note:As per our answering guidelines we  are supposed to answer only one question if multiple…

Q: Find the absolute extrema of the function on the closed interval. f(x) = 6 - x, [-2, 4] minimum (x,…

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