3. There are two conditions that must be met in order for a function to be continuous, explain those two steps by using an example.

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Q: S Consider the vector field F = Evaluate r(t) = t²i+t³j, 0≤t≤1 F-dr along the curve C:

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A: The given function .To find,(a)  at .(b) .(c)  at .

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Q: can you do this question again and include all the work, see if you get the same answer. include the…

A: The solution is shown in step-2

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A: An aircraft is flying horizontally at a constant height of 5000 ft above a fixed point. At a certain…

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A: The given vectors is .To find the vector that is opposite to  and has length .

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A: The solution is shown in step-2

Q: If C is a circle of radius 3 centered at the point ( 0, 4), then evaluate ƒ (7y — e³in (²) ) dx +…

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Q: ]]] (−2x + 4y+z) dxdydz

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Q: Find lim g(x) if g(x)=- x→4 [5√√x T if x #4 if x = 4

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Q: Evaluate the double integral f(x² + y²) dA. parabola y = x² and the line y = 2x. D is bounded by the

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Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 2 P4(x) =

A: we need to find the Taylor polynomial

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A: We are required to:

Q: Use the Limit Comparison Test to determine the convergence or divergence of the series. 1 Συντα 2. n…

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Q: Find a homogeneous linear differential equation with cons y = C₁ + c2x + c3e4x y"" - 5y" + 4y' = 0…

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A: As per our company guidelines we are supposed to solve first three subparts of a question so repost…

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Q: Evaluate

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Q: Find the values of a and b that make the following piecewise function differentiable everywhere.…

A: To find the values of  and  that make the following piecewise function differentiable everywhere.

Q: 3. The diagram shows the graph of the equation y = cotx. 14 -102 -11/4 0 mi4 m/2 31/4 11 514 3m Part…

A: Solving the problem

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A: To find the rectangular coordinates,  for point .

Q: 8. Use the 3rd degree Taylor polynomial centered at x = 0 for f(x) = e to estimate e and determine…

A: The Taylor series around x=a for function f(x) is given as

Q: 4. Evaluate the indefinite integrals. (a) / ( 1 + ²/2 + 1/1/7) dr 1 x2 (b) √ (e-²) -x/2 + cos…

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Q: 6. Trace the curve: r² = a² (1 + 2 cos ) (degrees) r Ⓒ (degrees) r e (degrees) r e (degrees) r 0 90…

A: Here, we have given a curve:We have to sketch the graph of the given equation.This equation is in…

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Q: Suppose your daily revenue from selling used DVDs is R(t) = 100 + 10t (0 ≤t≤ 5) dollars per day,…

A: The solution is shown in step-2

Q: 2) Find the derivative of each a. f(x) = 2tan¹(3-x³) b. y = 8in (2x + 8x - 2)

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Q: Consider the following. (If an answer does not exist, enter DNE.) f(x) = In(2 + sin(x)), 0≤x≤ 2π…

A: Given: To Find: To Find: To find the interval(s) on which  is concave up and concave down.To find…

Q: Given the sine function below, which statement is FALSE?

A: The amplitude of a function is the amount by which the graph of the function travels above and below…