Evaluate Dy tan(y) + 1 tan(y) - 1

Q: 28. After 500 years, a sample of radium-226 has decayed to 80% of its original mass. Find the half-…

A: Let A is original amount, A=100% Given t =500 year, At= 80%A At=20% half life h=?

Q: If ye cos x 8 lnx, find f'(x).

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Q: 2. lim x sin(1/x) X18 ex+2x 3. lim X18 ex

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Q: If two objects travel through space along two different curves, it is often important to know…

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Q: 4. When solving an auxiliary equation of a certain differential equation the roots m = 1 ± 2j are…

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Q: (a) dy Given 4 sin 3x + 2exy = (2x + y)³, find dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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Q: Q3/Find a volume for the region bounded by 4/X and Y = (X-3)² about the x-axis.

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Q: xdx (x + 1)²

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Q: Question 8 Using Simpson's method 2 √ ²x³ dx for n = 4 is equal to

A: Simpsons rule

Q: What is the equation of the line tangent to the function y = 2³+7x² + 5x - 2 at x = 0? There can be…

A: Application of differentiation

Q: evaluate the limit and simplify. Complete solution.

A: Evaluating the limit

Q: 4. When solving an auxiliary equation of a certain differential equation the roots m = 1 ± 2j are…

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

Q: Find the critical point and the intervals on which the function is increasing or decreasing and…

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Q: x³√/x² + 1dx

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Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

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Q: Question 2 Given a differential equation as d²y-5x dy +9y=0. dx² dx By using substitution of x = e'…

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Q: So x² dx √4-x²

A: To find out the integration.

Q: Q3/ Find a volume for the region bounded by 4/X and Y = (X-3)² about the x-axis.

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Q: 5. Find the volume of the tetrahedron bounded by the coordinate planes and the plane 3x + 6y + 4z -…

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Q: ind the general solution of xdy + (3xy + y - e-³x) dx 0

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Q: For questions no. 4 and 5. Given: Radium decomposed at a rate proportional to the quality of radium…

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Q: QI/ sin x a) find dy/dx for the equation (y 1+cos x b) find f'(x) for the equation f(x) = sec x

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Q: Determine the area of the triangle bounded by the coordinate axes and the tangent to ² - y = 0 at x…

A: Let's find area (A).

Q: (y² + 7xy + 16x²) dx + x²dy = 0 choices: In x + ( ₂₁ ₁²₁ ₁x) = C с 4x 1 In x + (y₂ + 4x) = с In x (y…

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Q: Refer to the given function below to answer the following questions: dr 0 de 2 = COS-

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Q: Solve for the variables using Gauss Elimination: -7a + 4b + c = 15 4a + 6b+ 5c = -6 3a-9c = 33

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Q: Using the linearity of the inverse Laplace transform, solve for the solution of the differential…

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Q: In (x-2) lim x2+ In (x² −4)

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Q: dy Classify the DE: xdx +xy= A) Separable and Linear (B) Separable but not Linear Linear but not…

A: Given differential equation is

Q: Find x, y and z, if the matrix A = a) x= 2₁ y= V₁ = √3 b) √√6 =√², y = x= 2= c) None of these d)…

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Q: 2. Find the general solution of xdy + (3xy + y - e-3x) dx = 0

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Q: Let f(x)=√3x-2 on the interval volume of the resulting solid. 83л (A - unit 3 135 83л (в -unit 3 125…

A: Region to be

Q: For questions no. 4 and 5. Given: Radium decomposed at a rate proportional to the quality of radium…

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Q: If y = arcsin (e5e), Check Answer dy da

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Q: x² - 2x² + 3x² -x +3 "x²³ - 2x² + 3 3

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Q: = 4 R is the region bounded by y = x², y = 4x - x² and the line x = and it is revolved about y = 0.

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Q: The reverse order of fo Say હરે e² dxdy is equal to e-1 8e None of them

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1 (A) 1 unit² B -unit² 3 -…

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Q: If f(x) = A B C -S sec²x D tanx l+et sec 3x √1+1² 1+e' 1+e lanx -dt, then f'(x) equals tanx 1+e In…

A: A detailed solution is given below.

Q: 은 J4-√x dx

A: This question can be solved using integration by substitution.

Q: The Minimum point of y = 3x+6

A: Given problem:- The minimum point of y=x3/(3x+6)   method:- We use first derivative test  When at…

Q: Which of the following can be determined given 3 A (f(x) = g(x)) dx 3 B [² (4f(x) +9h(x))dx с g(x)…

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Q: Evaluate the following indefinite integral using Partial Fractions S x² +4 (x²+4x+3)(x-2) dx

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Q: 15. The piecewise function -t+ + 0 st < 1 f(t) = ²+1 1st <2 -3 t22 can be expressed in terms of a…

A: This is a problem related to heaviside function which is also known as step function. Based on the…

Q: 9. Find the area between y = √x and y = √x+1, over the interval 0≤x ≤4

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Q: Write TRUE or FALSE before each statement. Solve y + y = ry³. Statement 1. The integrating factor is…

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: Suppose that f(x, y) = ²/" on the domain D = {(x, y) |0 ≤ y ≤ 1,0 ≤ x ≤y³}. D Then the double…

A: Given: fx,y=exy and D=x,y| 0≤y≤1, 0≤x≤y3   As we know the basic integration formula.…

Q: If given integrand is x² cos 2x dx and dv is equal to cos 2x dx, what is v?

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