Find the indefinite integral using the substitution x = 5 tan(0). (Use C for the constant of integration. √ √ 25+ x²0 X

Q: Given that u is a differentiable function, how do we get y' of y = arc csc(u)? T -^= f (x),n. (x),n.…

A: We can solve this as follows:

Q: Use the properties of logarithms to exapnd the logarithm as much as possible: 4 log5 ພາ2 x4y³

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Q: A series circuit has a resistance R = 10 Ohms and inductance L = 2. The battery gives a constant…

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Q: Let y=tan(5x + 4) Find the differential dy when z = 2 and da= 0.3 Find the differential dy when - 2…

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Q: 4. * f(x) = x² ex

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Q: 2. The area of Mammoth Cave Nationc Park in Kentucky is about seventy-four thousand, nine hundred…

A: We have given the area of the which is "Seventy-four thousand, nine hundred thirty and sixteen…

Q: 2 y=5 + x3

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Q: Sketch the region of integration and evaluate the following integral, where R is bounded by y = |x|…

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Q: By using the definition of the derivative, one can sin(x) - 1 x-x/2 2x - R Identify the correct…

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Q: Si 0 dx √√√x+1+1 7

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Q: Question 26 Find the second derivative (y") of the given function: y = e² sin z *)(2(- sin x)) e²…

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Q: Fill in the first 3 levels of Richardson extrapolation to estimate the derivative of sin(x) at x =…

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Q: Evaluate the following integral using trigonometric substitution. 9|N 9 2 0 dx 2 √√81-x² dx 2 √81-x²…

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Q: A sled is pulled along a level path through snow by a rope. A 30-lb force acting at an angle of 40°…

A: Work done by a force F unit acting at an angle x°, creating displacement of y unit is given by,…

Q: Question 2 Let f(x, y) = 5e¹* sin(3y) af д х af dy =

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Q: Conc.1 Conci .6. Find the intervals where the function concaves upward and concaves down, frx) =…

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Q: -1 y 3 2 (1, e) y = ex (1, 1) y = x¹ 1 2 3 X

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Q: b) Is the integral f x(In x) P sina de convergent? Explain why! a

A: To determine  whether the integral ∫01sin xx dx is convergent. To explain why.

Q: Find y' if 7 y² + sin (3x) = 12-y f

A: Here we can find the y' in the below steps, using implicit differentiation.

Q: Find the maximum value M of f(x, y) = x³y³ for x ≥ 0, y ≥ 0 on the line x + y = 2. (Use symbolic…

A: Given that fx,y=x5y3  ,x≥0,y≥0 To find : Maximum value on the line x+y=2Solution :we know that…

Q: Solve x + (3x + 1)y=e-3x dx Select one: O a. y = xe-3x + ce-3x O b. y = e-3x + cx-¹e-3x O c. y=e3x +…

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Q: For the function below, find a) the critical numbers, b) the open intervals where the function is…

A: A point x=a is said to be a critical point of f(x) iff f'(a)=0

Q: Classify the following DE's as Exact, Non-exact, Homogeneous or Bernoulli. A: (-xysinx + 2ycosx) dx…

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Q: 7/8x - 12 = -1/8x - 2

A: Given; 7/8x - 12 = -1/8x - 2

Q: Find the area of the region bounded by the y-axis, the line x=3, and the functions f(x) = (x² - 3x +…

A: We have to find the area of the region bounded by the y-axis, the line x=3, and the functions…

Q: Perform the following Operations on the Vectors= (-=-=-=-₁-3,₁-53₁ V² =<4₁-2,-17 W³² = (-4,04) R₁W=1…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: Find the solutions of the following IVPS or DE. a. y" — 4y' + 4y = e²x, b. y" - 2y = e2²x +3, y(0) =…

A: See the details solution in below

Q: Differentiate each function with respect to x -- Product Rule. Please express in descending powers…

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Q: 3) Find y" if y= 9 sin x.

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Q: Solvex - y = x² sinx dx Select one: O a y= cx? − xỉcosx O b. y = cx+xcosx O c. y = cx-xcosx Od. y=…

A: Topic = Differential equation Correct Option  = c

Q: The volume of a cube with sides of length s is given by V = s³. Find the rate of change of the…

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Q: Find the interval(s) on which ƒ(x) = |x² − 5x + 15 is differentiable. Enter your answer using…

A: The given function fx=x2-5x+15 We have to find the interval on which fx is differentiable.

Q: Find the rate of change of the area of a circle with respects to its diameter when the radius is 6/2…

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Q: Problem 1 Given a first-order differential equation: √1 + x² dy-ydx = 0 a) What is the best solution…

A: Sqrt(1+x2)dy -ydx=0

Q: f(x) X 2 tan r -

A: We have to solve given Questions.

Q: Let r(t) = (t², 1 — t, 4t). Calculate the derivative of r(t) · a(t) at t = 9 assuming that a(9) =…

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Q: Find the minimum of ƒ(x, y, z) = x² + y² + z² subject to the two constraints x + y + z = 1 and 2x +…

A: Given :- fx,y,z=x2+y2+z2Subject to constraints x+y+z=12x+3y+4z=8

Q: If a rock is thrown vertically upward from the surface of Mars with velocity of 25 m/s, its height…

A: The given data is: h=25t-1.86t2 Initial velocity u=25 m/s (a) To find the velocity of rock after 4 s…

Q: Write an equation (any form) for the quadratic graphed below 5+ y = 3 2 1 -5 -4 -3 -2 -1 + -2 -3 1 2…

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

Q: Find the derivative of the functions f(c)=xsinh-1 8/3 √9+x²

A: see below the answer and calculation

Q: Suppose that a population of bacteria triples every hour and starts with 300 bacteria. Find an…

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Q: Question 23 arctan y + ln(1 + y²) =a²x³: Find y': Gaz (1+²) 1+2y O Jamani No answer text provided. y…

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Q: Let f(x) = √28 - 4x and g(x) = 4x² — 2. • You must combine all like terms before yo your answer. •…

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Q: 1. (a) (b) Find and sketch the domain of the function f(x, y) = = Show that x²y² lim (x,y) →(0,0)…

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Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

A: Let x m be  length and y m be  width of rectangle  Perimeter of rectangle=2x+y m Area of…

Q: Question 21 Determine the derivative of the following curve: x² + y² = 5 Oy = -√2 Ov=√ Od = -√√…

A: Explanation of the answer is as follows

Q: Evaluate the following integral or state that it diverges. S4e - 4x dx Select the correct choice…

A: Given query is to find the value of the integral.

Q: Let f(x) = 0 for x < 0 and f(x) =x3 for x ≥ 0. Match the following. Here DNE means does not exist.…

A: Givenf(x)=0,x&lt;0f(x)=x3,x≥0We need to findf'(0),f''(0),f'''(0)

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing. f(x) = -2…

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Q: Let f(x) = √22 – 3x and g(x) = -5x - 9. • You must combine all like terms before you submit your…

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