The processor speeds, in megahertz (MHz), of one particular companies processors during the period 1970 to 2000 can be approximated by the following function of time in years since the start of 1970: v(t)={3t          0≤t<20 172t−3375     20≤t≤30 Compute limt→20−limt→20− v(t)=v(t)=  limt→20+limt→20+ v(t)=v(t)=

Q: Consider the Cobb-Douglas Production function: P(L, K) = 13L0.9K0.1 Find the total units of…

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Q: If  P=27/47 +r2 , determine the value of r for which P will be a minimum. Use the second derivative…

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Q: he average cost function is defined in economics as C¯(x)=C(x)x, where C is the cost of…

A: Given:  C(x)=0.01x3−0.4x2+13x+400,

Q: ! Find the max/min point for z = f(x, y) =-5x² -10y² + 20x+ 20y.

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Q: The consumer demand curve for Professor Stefan Schwarzenegger's dumbbells is given by  q = (106 −…

A: Given: The consumer demand is q = (106 − 2p)2, where p is the price per dumbbell, and q is the…

Q: Perform one iteration of the steepest ascent method to locate the minimum of f(x, y) = 4x + 2y +x? +…

A: given function fx,y=4x+2y+x2+2xy-3y2 with initial guesses x0=0,y0=0 claim- perform one interation of…

Q: Find the maximum sustainable harvest of the given function. f(S) = 24S025, where S is measured in…

A: Consider the given function fS=24S0.25 , where S is measured in thousands Suppose HS be the harvest…

Q: juice company has found that the marginal cost

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Q: f(x, y) = x? + y? + x²y+4.

A: f (x,y) = x2+y2+x2y+4      fx =0      ⇒      2x+2xy =0   — (1)      fy = 0      ⇒      2y + x2 =0…

Q: Find positive numbers x and y, whose sum is 75, such that xy2 is maximized.

A: Positive numbers x and y,x+y=75xy2 is maximized

Q: Find the marginal average cost function of each function defined as follows.

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Q: By the use of local linear approximation of g at x=2, estimate g(-1.998) if g(-2)=-1 and g’(-2)=10

A: local linear approximation formula for g(x)g(x)=g(a)+g'(a)(x-a)

Q: The consumer demand curve for Professor Stefan Schwarzenegger's dumbbells is given by q = (101 −…

A: Given:Demand equationq=(101-2p)2

Q: 27The platis that passes through the e Point C672) and contains the lihie メー4-2t)X= 345t) Zと+4t 4. こ

A: We have to find the equation of the plane which passes through the given point and contains the…

Q: Findthe absolute minimum on ico, ae) fon f (x) =x+l6,

A: Critical points of the given function can be found if dfdx=0 fx=x+16x Differentiating the function…

Q: 2. Find the family of orthogonal trajectories of the given family of curves in the following…

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Q: Find the 4th iteration value of an extremum (maximum/minimum value) of f(x) = 0.25sinh(2x) - bx² -…

A: The function given is as follows: fx=0.25sinh2x-bx2-cx+d Where, b=3, c=5, and d=6. Hence the…

Q: At what point does the following function have a local maximum? f(x, y) = 3- 8x +18y-4x2-9y2 О a.…

A: Proceed as shown

Q: The Cobb-Douglas production function for a particular product is N(x,y) = 80x°y3 where x is the…

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Q: The consumer demand curve for Professor Stefan Schwarzenegger's dumbbells is given by  q = (102 −…

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Q: All units in a 30-unit apartment building are rented outwhen the monthly rent is set at r =…

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Q: Find the orthogonal trajectories of the family of 1 curves Y= X + k

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Q: A manufacturing company produces two models of an HDTV per week, x units of model A and y units of…

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Q: show steps please.

A: We will find the first two derivatives of F(x) We use the fundamental theorem of calculus To find…

Q: The consumer demand curve for Professor Stefan Schwarzenegger’s dumbbells is given by q = (118 −…

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Q: Find Positive nombers X$ Y Such that X+y = 78 and 24xy a is maximized

A: To find two positive numbers 'x' and 'y' such that,  x + y = 78     =&gt; y = 78 - x And such that…

Q: Find the minimum and maximum values of the function subject fCx.y) =6x?+Sy? to the given Constreant…

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Q: A juice company has found that the marginal cost of producing x pints of fresh-squeezed orange juice…

A: Given marginal cost function, C'x=0.000008x2-0.004x+5, for x≤350 Find the total cost.

Q: find the formula for a function of the form f(t)=at+b/t with a local minimum at (3,3) and a local…

A: For critical values of f(t), f'(t)=0Critical values of f(t) are t=-3 and t=3So we find f'(t) from…

Q: 14. Show that f(x) x+4 never intersects its horizontal asymptote. %D 3x+1

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Q: If f(x) = x - ka 1 has a relative maximum at r = -2, then the value of k is

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Q: Which of the following is the isogonal trajectories of the one-parameter family of curves y(x-a) = 1…

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Q: The number of people P(t) (in thousands) infected t months after an epidemic begins 5 - where…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly aks…

Q: Find the critical points of the function f(r, y) = 8y3 +12x2 – 24ry and classify them as local…

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Q: A small business determined that the price-demand and cost functions for producing and selling x…

A: Given that, The price demand function is px=70-0.25x and the cost function is Cx=0.5x2+10x+800. We…

Q: At what point does the following function have a local maximum? f(x. y) = 3-8x + 18y-4x2-9y2 O a.…

A: Given: f(x, y)=3-8x+18y-4x2-9y2

Q: Find the critical point(s) of the function f(x, y) = -2r³ – 4ry + 2x – 5y – 1 and classify them as…

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Q: Find the critical numbers of the function. s(t) = 3t* + 201 - 182

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Q: If (a,B) is a saddle point of the function f(x,y)=27y2-y3+3x²-6xy, then a+ß=

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Q: A juice company has found that the marginal cost of producing x pints of fresh-squeezed orange juice…

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Q: For what values of a and b does f(x) = a(x- bln a) have a local minimum at the point (2, 5)? Figure…

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Q: The demand for nurses in the US between 2000 and 2015 is estimated to be: D(t) = 0.7t2 + 0.265t +…

A: Derivative indicates the rate of change. Positive derivative meaning positive slope, which indicate…

Q: If (a,B) is a saddle point of the function f(x,y)=21y2-y3+3x2-6xy, then a+ß=

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Q: Aki's Bicycle Designs has determined that when x hundred bicycles are​ built, the average cost per…

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Q: If 0 = KHLV-, where k is a constant, and there are possible errors of ±1 per cent in measuring H, L…

A: We will find out the required value.

Q: Q2. The following tables give the velocity data for the space shuttle between lift-off and the…

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Q: The consumer demand curve for Professor Stefan Schwarzenegger's dumbbells is given by  q = (87 −…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.