Exercise 3. If x₁,..., Xn E RK, prove that x₁ ++Xn ≤|x₁| ++|xn|.

Q: The graph of f(x) is shown below. Estimate and list the value(s) of x where f(x) has a horizontal…

A: The graph of fx is shown below. To estimate and to list the values of x where fx has a horizintal…

Q: 2. 2 구 1 (x-4)2, (y+5) 10 (1+5)-1 구

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A: Given:- fx=5-x , gx=x2-4x

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A: Given query is to find the value of k that makes function continuous everywhere.

Q: Use the graph to determine the limit. (If an answer does not exist, enter DNE.) y (4,4)

A: We are asked to find the limit of the function from the graph

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A: Given graph is

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Q: 41. lim [In(1+x¹) - In(1 + x)] 110

A: We need to find limit.

Q: Given: x2 O 1.5 O 2.5 dy dx = 4 x² + 7xy + 2y2, Find C if y = 1, x = 1 O 3.5 O 0.5 O None of the…

A: see below the answer and calculation

Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

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Q: Differentiate the function. A(s) = -- A'(s) = 44 5 X

A: Given: The given function As=-11s4 To find the derivative of the function. Derivative formula:…

Q: Find the derivative of the function using the definition of derivative. f(x) = x³ − 3x + 7 f'(x) =…

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Q: Form a polynomial whose zeros and degree are given. Zeros: 2, 2, 6; degree: 3 Type a polynomial with…

A: Given query is to find the polynomial.

Q: Find the area of triangleABC if <C = 30 degrees, a = 4, and b = 5

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Q: 1. A. f sin 2x cos 5x dx B. f cos 2x cos 3x dx c. ftan³x sec5x dx

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Q: Find the volumes of the solids generated by revolving the region in the first quadrant bounded by…

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Q: The graph of a function f(x) is given as follows. 4 3 2 1 1 2 3 4 Enter the value of each of the…

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Q: xy² = x + cx³

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Q: yete (t+3)− −¹+0 e Solve for y. ye-¹=(-t-4) et+C

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Q: Find the domains and ranges of f, g, f+g, and f g for the functions f and g below. f(x)=x,…

A: Solution ) f(x) = x , g(x) = √(x - 22 )  1) domain of f  We can independently put any value of x…

Q: B)Z = 1 + e, find |Z|.

A: Let's find.

Q: 1. Find the DE of each of the following by eliminating the arbitrary constants. y = Get + C₂ cosx +…

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Q: Solve the following initial value problem for r as a function of t. d²r Differential equation:…

A: The given equation is; d2r/dt2=5eti-e-tj+18e3tk.

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A: If any constant number is divided by infinity, then its value will be ZERO.

Q: Given the quadratic equation y = 7 - x - 3x². a) State whether it has a maximum or a minimum value.…

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Q: Show algebraically that lim 818 2 x² - 2 - x = 0.

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Q: (a) Show that E(x) = f(x) + f(-x) is an even function. (Simplify your answers completely.) E(x) =…

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Q: Find the general solution of each differential equation. x' X = t² + tx+x² 2t² + tx

A: Given x'=t2+tx+x22t2+tx

Q: = Use the four-step definition of the derivative to find f'(x) if ƒ(x) · You may have to simplify…

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Q: Evaluate: * 1 2 z² dz z²+3z +2 -6лi 3лi inside the circle |z| = 4 4 3 -6 πί

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Q: 4x +4x+1 lim x--1/2 2x+1 (ax + 3bc), where a, b, and c are constants

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Q: Q2 Find the values of x for which the series converges 3n xn a) En=0 n!

A: The given power series: ∑n=0∞3nxnn!We will basically find the interval of convergence.

Q: Ex-ylny + y lnx) dx x (lny - Inx) dy + X XY =

A: solution

Q: Give examples of concepts, priciples and formula of the mensuration of plane figures Please make…

A: Mensuration: It is branch of the Mathematics which deals with the measurements of length, perimeter,…

Q: Determine whether the function x² +3 (x - 1)² is even, odd or neither. h(x) =

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Q: Is the function continuous at x = -1? O Yes O No

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Q: Find the solution for following variable separable equation: dy/dx = (y²-1)/(x²-1), y(0)=0

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Q: 2. a). Show that e2x and e³x are linearly independent solutions of the ODE y" + 5y +6y= 0 and find…

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Q: Use the graph of the function f shown to the right to find f(-2), f(-1), and f(0). f(-2)= f(0) = ...…

A: We have to find the value of function at the given values.

Q: Find the constant values of m and n if 2y = 2nx² + 2mx given that when x = 1, y _0 and = 14. dx

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Q: y = (c1 + c2x + c3x²)e³x

A: Topic = Differential equation

Q: For step three, how did you replace the h?

A: Let's solve.

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Q: Identify and draw the domain of functionf(x, y) = = √4-x²+4y² 2 In (9-x² - y²)

A: The given function is: f(x,y)=4-x2+4y2ln9-x2-y2