47. lim- v-3 48. lim y-2 49, lim x-2 v-1-√²-5 v 3 y²+y-6 50. lim x 2 50 51. lim x18 8-y²-y x² - 4x + 4 - lima sin²Tx 3x+2-2 x-2 x² - ln(2/x) 3x² + 2x 1 1

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A: g(-2)=5f'(5)=-1/2Find g'(-2).

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A: To calculate the first four terms of the following sequence, starting with .

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A: Let, To determine the value of the following limit.

Q: Find and classify the critical points. 12 H(£,y)=re +y* – 12,

A:

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A: A manufacturer of lighting fixtures has daily production costs of C = 800 - 30x + 0.75x2, where C is…

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A: To find the absolute maximum and absolute minimum value of the function  in the interval .

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A: f(x)=−3x4−20x3 on [−7,−2]

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A: Let  denote the vector  and  be a fixed positive constant.To compute where  is the vector field…

Q: 13. If f(x) L x-1 x #1 4, x = 1 lim f(x) exists which of these statements are true? II. fis…

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A: Consider the following.To find the equation of the given ellipse.To find the foci of the ellipse.

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Q: Which linear function is represented by the standard form equation below? 4x + 5y=40 A f(x) = -x+8 B…

A: the standard form of equation is 4x+5y=40

Q: Let lim g(x) = -6 and lim h(x) = 6 x 4 x→4 Determine the value of the limit lim 2+√xh(x) | √xh(x)] x…

A: Let .To determine the value of the following limit.

Q: So 0 xe- dư x²

A:

Q: 4

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Q: Find the critical numbers of the function. (Enter answers as a comma-separated list) f(x) = x3 +…

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Q: Consider the function f(x): = x² + 4x + 3 x-3 a. Find the first derivative. f'(x) = b. List any…

A: Consider the function .(a) To find the first derivative.(b)To list critical values.(c) To identify…

Q: Find the average height of the paraboloid z = x² + y² over the square 0≤x≤2, 0≤y ≤ 2.

A: To find :-The average height of the paraboloid  over the square

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A: Consider the fucntion

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Q: The value of c that satisfies the Mean Value Theorem on the interval [0, 5] for the function f(x) =…

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Q: If f be the function defined by f (x) = x³ + x. lf g (x) = f−¹ (x) and g (2) = 1, what is the value…

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Q: Find dx/dt, dy/dt, and dy/dx for  x=5t^3+6t, y=4t-3t^2

A:

Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = 3 sin(x) + 3 cos(x),…

A: Consider the function (a) The intervals on which the function is increasing or decreasing can be…

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Q: 20. The radius of a sphere increases at a rate of 1 m/sec. Find the rate at which the volume…

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Q: Find the interval in which the function is X decreasing f(x) = 2²+4 ○ (2, ∞) O (-2,2) ○ (-∞0,00) O…

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Q: 24) A wire 1 metre long is to be cut into two pieces. One piece is to be formed into a circle and…

A: It is given that the length of the wire is 1 metres and it is cut into two pieces.Let the length of…

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A: Given that line passes through the point  and parallel to vector

Q: Convert the point from rectangular coordinates to spherical coordinates. (-1, 2, 1) (p, 8, 4) = ( X

A: The point in cartesian coordinate is given byTo determine: The point in spherical…

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Q: If g(x) = x + y², and R= [0, 1] × [0, 2], compute the value of SSR 9(x, y)dA. -23/6 19/6 11/3 22/3…

A: The given function , and the region .The objective is to find the value of the integral .

Q: Find the second smallest positive x-value where the graph of the function f(x) = x + 2 sin(5x) has a…

A: to find the second smallest positive value of x where tangent line to f(x) is horizontal.

Q: f(x) = 2 ≤ 2

A: f(x)={6x,, if x<1ax2+b, if 1≤x≤27x, if x>2

Q: Use the graph shown to find the following. (a) The domain and range of the function (b) The…

A: As we can see from the graph, the vertical asymptote is: x=1So the domain is

Q: Let g(x)=x√100-² A+ B² (100-³² 0(x) A- BM C- 0'(x)= D= E- Dx² + Ex (100-y where Find the relative…

A: The given function isA square root function  is defined only for x0.So, the given function is…

Q: EXAMPLE 5 If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional…

A:

Q: The graph below shows the velocity of an object (in ft/sec) as a function of time t (in seconds).…

A: We will find the displacement.