It was determined that the number of prey consumed by a predator over a period of time was a function of the prey density,  x ( number of units of prey unit area), such that f(x)= 10x/1+0.1x If the prey density were to increase without bound,  what value would f(x) approach?

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A:

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Q: If the critical point of the function f(x.y)-x- y- 2xy +6 is (0.0). test this point whether it is:

A: We use second order partial derivative to know about critical point behaviour

Q: It was determined that the number of prey consumed by a predator over a period of time was a…

A:

Q: Suppose f(x)=6x2+9x−13. Write an expression in terms of x and h that represents the average rate of…

A: Average rate of change is ratio of change in function values and time interval.

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Q: Find the local and absolute extremum for the functions over their domain: 5. f(x) = vx2 + 8x + 20

A:

Q: Find the local and absolute extremum for the functions over their domain: 1. f(x) = x2 – 6x + 8

A: Given

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A: Given that

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A: We have to find domain

Q: Consider f(x) = 3X. What is the best approximation for f'(2)?

A:

Q: The tangent line to the graph of f(x)= 5-x+e^(x-1) is horizontal at what  point?

A: Calculus Question

Q: Find the Quadratic approximation of the function at the given value f(x) = 1n(x + 1)     near a = 0

A: Given  The function is f(x) = ln(x + 1)     near a = 0 .   Formula for Quadratic approximation :-…

Q: If the total revenue function for a blender is R(x) = 41x – 0.01x² where x is the number of units…

A: Given that, the revenue R (in dollars) for a blender is given by  R(x) = 41x - 0.01x2 where x is the…

Q: Find the inflection points of the function f(x) = ln(x^2 + 1)

A:

Q: The best suitable method to approximate a zero of the function f(x) = e* – 1 is:

A: Given f(x) = ex - 1

Q: The best suitable method to approximate a zero of the function f(x) = e* – 1 is: |

A: Given,                 f(x)=ex-1

Q: Consider the production function:           Y = 0.75X + 0.0042X2 – 0.000023X3 (a) At what level of…

A:

Q: Find the domain of function defined as follows. y = ln(x + 7)

A: Given       y = ln(x + 7)

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A: Given: fx=x-4x+4, To find: The expression of average rate of change of f over any interval x,x+h.

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Q: 3. Armaan claims that the functions f(x) = 32x + 5 and g(x) = 32* + 8 have different instantaneous…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: An articlet in The New York Times states, "The number of gas stations [in a city] grows only in…

A: We will use the given relation between population and gas station.

Q: Total net shipments of aluminum (in billions of pounds) are approximated by g(x)=16.2+2.86ln(x+1)…

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Q: 6. find all local extremum value in this function f(x)= xʻe* م م م م و و ه و و و و و و ه و و و و و و…

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Q: The population, f, of a small community on the outskirts of a city grew rapidly over a fifteen year…

A: Newton's backward difference formula uses the formula below to approximate f(x) .…

Q: Find f' (æ) for f (x) = 7 ln(4 + æ²).

A:

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Q: Find f''(x) for: f(x)=ln⁡x/4x

A:

Q: #3 Find the instantaneous rate of change for the function f(x) = V3 – x at x = -6.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 1. Use the second derivative test to find the relative extrema of the following function. f (x) =…

A:

Q: Find the rate of change of the function at a given value. 1. f(x) = 2x – 3, at x = 5 2. f(x) = x² –…

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Q: Find the absolute extreme values of the function on the interval. f(x)=ln(x+2)+1/x , 1 less than or…

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Q: 2. Determine the zeroes of 2 x² = x f(x) instantaneous zeroes using a table of values. — 3x 4 and…

A: To find the zeroes of the polynomial.

Q: find the instantaneous rate of change for the funtion at the given value g(x)=x+11x-15 at x=1

A:

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Q: Find the local and absolute extremum for the functions over their domain: 2. f(x) = x3 + 4x2 – 11x –…

A: Given function is  f(x)=x3+4x2-11x-2

Q: Suppose f(x)=x−1x+6. Write an expression in terms of x and h that represents the average rate of…

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Q: There is a relationship between perceived corruption and human development in a country that can be…

A: Given  H(x)=0.3+0.28 In x                 where H(x) is Human development index…

Q: Given the function f(x) = x2/3, which of the following is a valid formula for the instantaneous rate…

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Q: Find a good numerical approximation to F(4) for the function with the properties that F'(x) = e-x+15…

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Q: Show that a function f decreases most rapidly at x in the direction opposite to the gradier (that…

A: Solve with given conditions

Q: 1. What is the average rate of change of the function f(x) = x² - 4x + 7 on the interval 1 ≤ x ≤ 3?

A: average rate fo change in an interval (a,b) =f(b)-f(a)b-a

Q: Estimate the instantaneous rate of change of the function f(x) = x² – 4x +3 at x = -3 using the…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.