Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is infinite, enter '∞' or '-∞', as appropriate. If the limit does not otherwise exist, enter DNE.) lim x→2 f(x), where f(x) =    10  −  2x    if x < 2 x2  −  x    if x ≥ 2

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A: ordinary differential equation include ordinary differential equation (ODE) contain one variable and…

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Q: -5 -5-4-3-2-1 Evaluate. 45 lim f(x) x-1 45

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Q: Find the General Solution G.S. 1. (2xy - 3x²) dx + (x² + 2y)dy = 0 2. 6x + y²) dx + (2xy − 3y²)dy =…

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Q: 2 (2xy-3x²) dx + (x² + 2y) dy = 0

A: We have to find the solution of the following differential equation in x and y.

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Q: 9. n=1 1

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Q: Find

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Q: 27. n=1 1 n+√n

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A: Sum of all angles in a triangle= 180 degrees

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Q: Indicate whether the following equations are true or false for all integrable functions f. a) b) c)…

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Q: Use the graph of y=f(x) to graph the function g(x) = -f(x)-1. y = f(x) Ay d 2 Choose the correct…

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Q: In Exercises 5-14, determine the convergence of the given series using the Ratio Test. If the Ratio…

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Q: Q3/ Use the l'Hopital's rule to find the limits 1-sine 3) lim 8-π/21+cos20

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Q: Given: f(x)= = 1 2¹ and g(x)=√x +3 2-x Find the domain of f(g(x))

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Q: (c) (yez-e-) dx + (xe-+e) dy = 0 2x 608 16- 213 sec² 2 du

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Q: 19.) Differentiate f(x)= (3x - 5)*(7-x) 10

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Q: Show that the function f(x) = |x - 21 is not differentiable at 2. We have The right-hand limit is…

A: To show that the function fx=x-2 is not differentiable at 2.To find a formula for f' and to sketch…

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Q: Help Entering Answers Find the length of the curve: where 1 < t < 4. Length = M r(t) = 9ti…

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Q: the limit is positive or negative infinity. If the limit does not exist as a finite number or as…

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Q: Find the instantaneous rate of change of the function f(x) = x3 + 8x when x = –3

A: Find the instantaneous rate of change of the function f(x) = x3 + 8x when x = –3

Q: Find differential equations for the following families of curves: (a) x2 + cy² = 1, (b) y² = ax + b.

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Q: An amount of $500 was invested in 1995 and the investment grew as shown in the following table.…

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Q: 6 2²{ - 2s-8) 01 02 03 C 4+2 ett

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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: xy'= y inx

A: xy'=ylnx

Q: 18.) Find the derivative.

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Q: Destiny is eating lunch at her favorite cafe when her friend Jada calls and says she wants to meet…

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Q: 6.) Find the limit (if it exists). 6x² + 3x + 10x²+x+ lim x+²)

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Q: Find the general solution of the Differential Equation dy dx 4y x(y-3)

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Q: What  is the equation of the circle with center (1,-5) and radius of 7?

A: As we know that; The standard equation of the circle is: x-h2+y-k2=r2 Where the Center is at h,k and…

Q: For the given function f(x), the point c, and a positive number e, find L= lim f(x). Then find a…

A: Let's find value of L.

Q: Determine algebraically whether the function is even, odd, or neither even nor odd f(x) = - 0.72x^2…

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Q: Evaluate 4 fa²¹ t tan³ (x5) dx

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