Evaluate the limit: lim, +∞ (e² + x) =

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A: Given series:- ∑n=1∞an=∑n=1∞4Pn5n

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Q: (a) Prove that F(x, y, z) = (y² cos r+z³)i+(2y sin r-4)j+(3r2+2)k is a conservative vector field.…

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Q: Consider the point (음, %) Fort 1. Find (sc (t) A).& 10 22-1 B) 은 C) - 음 이응 Ja 100 0)-10 F) - g) none…

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Q: 1) Consider the function f(x): = 5x² - 4x +7 Find a number c in the domain such that f (c) = defined…

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Q: 5. Determine the location and value of the absolute extreme values of f on the given interval, if…

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Q: 6. $2 wwwage 2+1 3335

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Q: what is math

A: Definition of mathematics

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A: let at any moment base distance = x height of top end of ladder at any time = y ladder height = h…

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Q: Determine whether the integral is convergent or divergent. 3 36 √3-x O convergent O divergent dx If…

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Q: 3) Consider the function G(x) = f g (t) dt. Find the derivative G' (x). O g(x) g(x)-g(1) O g(t) O…

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Q: Evaluate the limit: lim+∞ In √x+5x 7x

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Q: Describe and sketch the following set of points defined by the following conditions. (x + 2)² + y² +…

A: Given : we have a surface     (x+2)2+y2+z-12=9 and with the conditions :   x≥-2, y≥0, z≥1    To find…

Q: Find a power series representation for the function. 8 + Χ (1 − x)2 f(x) Σ( 1) η Determine the…

A: The given function is: f(x)=8+x(1-x)2

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Q: . 6. Consider the function f(x) = r³ - 2x2 defined on the interval [0, 1]. Find the point(s) on the…

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Q: Use the linear approximation of f(x, y) = e²x²+2y at (0, 0)

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Q: 1) Use the Comparison Test to determine whether the infinite series is convergent. ∞     k = 2…

A: Comparison Test:- If a series of the form ∑n=1∞an is given. Also if we know that ∑n=1∞an≤∑n=1∞bn…

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A: we need to write down the differential equation by eliminating the arbitrary constant.

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Q: SHOW COMPLETE SOLUTION A right circular cylinder is given. A slice perpendicular to the bases…

A: As we know that Volume of a right circular cylinder is πr2h, where r and h are radius and height of…

Q: fix√x²+2x+5dx

A: To evaluate the following integral. ∫13xx2+2x+5 dx

Q: 2. The position of a rider on a Ferris wheel is an example of periodic motion. Find three other…

A: 1 )A Rocking Chair

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Q: Use the graph of the function to estimate the interval on which the function is increasing. y -SA-…

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Q: (c) Check that your solutions t substituting the expression 63. xy + 2x + 3x² = 4

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Q: 1. Evaluate the following integrals: 5/2 d. S3 1 1/2 2 2x -x -dx

A: The integral is  ∫1/25/2 12x3-x2dx

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Q: Determine the vertex, focus, directrix and axis of symmetry of the parabola with the given equation:…

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Q: 1 1 Calculate the gradient of h(x, y, z)=33 Vh= ← 1

A: calculate the gradient of h(x,y,z)=1x2.1y3.1z3