1.1 Determine the following derivatives with respect to x 1.1.1 y = cos(sin(cos.x)) 1.1.2 y=(x²-1)*(x²+1)*

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Q: uestion 4 (a) Solve the following: 4x*dx (b) Explain with the aid of a sketch how this value can be…

A: A detailed solution is given below.

Q: Solve the following Differential Equations with Laplace Transforms y" - 6y' + 15y = 2 sin(3t), y (0)…

A: Let's solve diffrential equation by using laplace transform.

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Q: Investigate if the integral is convergent or not. Justify your answer.

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A: Hee, the given expression is: limx→0+ln xx

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A: The solution of the integral is given below:

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Q: Find a scalar equation of the plane x + 2y + 3z = 0 -x+ 3y - 2z = 0 c. 13x + y - 5z = 9 d. 13x+y- 5z…

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Q: 1- Calculate the area of the region which is bounded by: y = (x - 1)², y = (x-4)2, and y = 0.

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Q: 19. Find x from the following equations: 27x = 9y 81*3-* = 243 A. 2.5 B. 2 C. 1 D. 1.5

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the average value of the function f over the interval [0, 15]. 4 f(x) = x + 1

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Q: Find the orthogonal trajectories of x = C exp (-y²). Oy=C*exp(-x) Oy=C*exp(2x) Oy=C*exp(-x^2)…

A: Given problem:- Find the orthogonal trajectories of x = C exp (-y²).

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A: To find interval of convergence of ∑n=2∞ (x−2)nln⁡(5n) Let an = ∑n=2∞ (x−2)nln⁡(5n) Therefore, an+1…

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A: It

Q: QY/ Find the direction devivative of f(x,y) = x₁² + yet at the paint (2,1), by the dirction of V =…

A: We have to find the directional derivative.   According to our guidelines we can solve only one…

Q: H.W: show that the equations are homogeneous and solve: 20 2. x² dy + (y² - xy)dx = 0

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Q: lim-0 OI Oll O III OIV e² - x Not Indeterminate کے

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Q: f5(x³ + x)⁹ (3x² + 1)dx O 5(x³+x) ¹0+C 10 (x²³+x) ¹0 10 +C O 45(x³ + x) +C O(x³ + x)¹0+C

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Q: Q22) The inverse Laplace transform of H(s) : = a) f(t) ==e¹+¹e²t 8 8 -3 c) f(t) == est +²e-2t 8 8 1…

A: To find the inverse laplace transform of givem function.

Q: 3. Waile si Sigma Notatimi 1. 12-201 4 곱 so times 나스

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Q: Find the function f given that the slope of the tangent line at any point (x, f(x)) is f'(x) and…

A: This question is related to Functions and application of integration, we will solve it using given…

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Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate…

A: We have to find the series is convergent or not and find the sum also.

Q: lim x→0 1 x + S x 6571- S Ans 50.

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Q: Question 4 (a) Solve the following: √4x¹dx (b) Explain with the aid of a sketch how this value can…

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Q: Question 4 (a) Solve the following: 4x¹dx (b) Explain with the aid of a sketch how this value can be…

A: we have to find the value of integral ∫-22 4x4  dx

Q: Use the Laplace transform to solve the given initial-value problem. y'' + 2y' + y = 0,  y(0) = 1,…

A: A detailed solution is given below.

Q: 17. The general solution of the equation (x³ + 3xy²)dx + (3x²y+y³)dy = 0 is A. (x4 + 6x²y² + y4) = C…

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Q: P2: Calculate the volume of solid of revolution when the region bounded by y = √√x + 4 and x - 2y +…

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Q: Consider the following initial-value problem. f'(x) = 8ex − 4x; f(0) : = 13 Integrate the function…

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Q: 10- There is a rectangular playing field in Alaska Denali Park for a grizzly Bear with an area of…

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Q: Find y': COS X y = 1-sin x O y' = sin² -sin x-cos² x (1-sin x)²

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Q: Given: y = = 4 cot (3 - 2x) Find: dy dx 0-8 csc² (32x) O csc² (3-2x) 08 csc² (3-2x) -4 csc² (3-2x)

A: Given y=4cot(3-2x)To find dydx:

Q: 2. The base of a solid is an ellipse whose major axus and minor axis are 12 cm and 8 cm long,…

A: We need to find volume.

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

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Q: Solve the following equations 2)3x+2 = 27 1) 2Ln(√x + 3) + 2Ln(√x-1)=Ln(6x-7) I 1 1

A: Let's solve both equation.

Q: Solve the following Differential Equations with Laplace Transforms y" - by' + 15y = 2 sin (3t), y…

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Q: Which of these series, if either, diverges? ∞ - 1)k 1. II. Σ(-1)^ (77) K²+1 k=1 k k=1 A. I only B.…

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