Solve the integrals: (1) (c I₁ = 1 |x| x² + x| dx

Q: 20.) Differentiate. f(x) = +3 -2

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Q: 3. Check for homogeneity and obtain the general solution. (Let 4C=C) (x² + y²)dx + xy dy = 0

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Q: Given f(x, y, z) = xyz, find fyyx

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Q: Solve for the complete solution of the differential equation: y" + 4y + 5 = 0; y(0) = — 2, y'(0) =…

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Q: 29. Σ n=1 n In2 + 4η + 1

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Q: x that makes each statement true. 15. 3 - 2 -X 4 = - 9 16. y². y² =

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Q: (b) dy 3-4012 4xy + by2 ; dz = (1) y(1) = -1

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Q: Integrate: 16-y4 y³ - dy

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Q: The graph of the function f(x) is shown below. f(x) f(-1) is f(0) (a) Using the figure, find the…

A: Here we have to use the concept of derivatives

Q: Using the appropriate theorems, explain why the function is continuous at every number in its…

A: Given function, f(x)=2x2-x-2x2+4 Function is undefine if x2+4=0x2=-4x2=4i2x=±2i∉R

Q: 2. Consider the equation du = -0.5y²(y² + 1)(y² − 4)(y + 1)esin y (a) Find all equilibrium…

A: To find the equilibrium solution of the differential equation , set the differential equation to…

Q: (a) Find the general solution of dy/dx = 8x³-4x+1. (b) Determine the particular solution such that…

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Q: 5² S d't ds² + St dt ds =S

A: Given:      s2d2tds2+stdtds=s

Q: Find dy dt || dy dt for y = sin 2 (3nt – 4).

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Q: Kindly exhibit that xzxx+yzxy=y2zyy if z=xy+yln(xy)

A: The given data is: z=xy+ylnxy To prove: xzxx+yzxy=y2zyy

Q: = Find the GS of 2xyy' + y² + tan x = = 0

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Q: Find the particular solution of each of the following. y(1+21n²) dx+xdy=0; y(e)-e

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Q: (d) d dy 11 = 4- 2x cos y 3y² tan 2x - - 2y3 sec 2x 2 sin y

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Q: 7. AT 0=1 n n + 1

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Q: Use Gaussian elimination and Gauss Jordan method to solve the system of linear equation. x - 2y-6z =…

A: The given system of linear equations, x-2y-6z=122x+4y+12z=-17x-4y-12z=22 We have to find the…

Q: 1. A carpenter can construct book cases at a cost of P400 each. If the carpenter sells the book…

A: Given:- Carpenter sells the book cases for x pesos each And 300-2x book cases will be sold per month…

Q: Find the slope of the tangent to the curve y = 3 + 4x2 - 2x3 at the point where x=a .

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Q: dy Write the function below in the form y=f(u) and u = g(x). Then find as a function of x. dx y = -…

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Q: (x + 2y — 2) dx + (2x + y + 5) dy = ○ (x + 4)² − 2 (x + 4) (y − 3) + 4(y − 3)² = C O (x+4)² + 2(x +…

A: We have to find the solution of the given differential equation.

Q: Question 1: Let f be a function and let h be a non-zero real number. Then the derivative (when it…

A: We have to tell true or false Answer (1)

Q: f(x)=2x-1 9X+1

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Q: 2 Determine the equation of the line tangent to the curve y = 4x + X y = at the point (2,9).

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Q: 3) A university has 10 lecture halls. Each lecture hall has 15 rows of desks supo de With 5 desks in…

A: totak lecture halls=15

Q: for the function f(x) = 7X+9 and (exact answers) find the following 1. f(g(x)) = 2₁ g (f(x)) = 3.…

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Q: 3. Let y = (f(x) + 5x²)4 and suppose that f(-1) = -4 and = 3 when x = -1. Find f'(-1). dx

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Q: Name: 1. Find the value of b for which the given equation is exact. Then solve it using that value…

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Q: The area of the top side of a piece of sheet metal given below. The sheet metal is submerged…

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Q: Find a general solution to the differential equation: dx/dt = = x + e^t -- please show all work in…

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Q: 2. Find the solution of the IVP: (1+y cos x) dx - sin a dy = 0, y(n/2) = 1. Then, evaluate y(1.603).

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Q: (a) cos(0) = (b) tan(0) (C) sec (0) (d) csc (0) (e) cat (A) =

A: Topic:- trigonometry

Q: the function y = x(x 6)².

A: To find the critical points for the given function

Q: 3)Find a function whose graph is a parabola with vertex (3, 1) and that passes through the point…

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Q: Evaluate the expression 3-³6².

A: Given, 3-362

Q: - If f(x) = 4x² – 20x + 21, evaluate_lim_f(8 + h) − f(8) h→0 h If an answer does not exist, enter…

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Q: (a) Show that y = e(c₁ cos x + c₂ sin ) is a general solution of y" + 2y' + 2y = 0. (b) Deter- mine…

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Q: 86. f(x) = √x, g(x) = 2 x - 4

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Q: 1 23. Σ (Inn)" 0=1

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Q: 3) Use the appropriate integral formula for the length of a curve represented by a function y = f(x)…

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Q: A curve passes through the point (0, 2) and has the property that the slope of the curve at every…

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Q: 4. A large container initially contains 50 gallons of salt-water with concentration 0.4 lbs. of salt…

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Q: Find the position vector R(t) and velocity V(t) given the acceleration A(t) = 25esti + 5 cos(t)j +…

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Q: 3x-2 X→ 4x +3 Evaluate Lim A. 4/3 B. 3/4 C. 5/4 D. 1

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Q: " + 4y = cos 3x

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Q: Find f'(a). f(x)=√1 - 6x

A: f(x) = 1-6x here we have to derivate this function we use chain rule for that  further given in…

Q: Integrate cos x dx with limits from 0 to π/2. A. 1/2 B. 3/2 C. 1 D. 2

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