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 per unit area), such that f(x)=10x/1+0.1x  If the prey density were to increase without bound,  what would f(x) approach?

Q: 1) Find the second derivative for the following functions: a) f(x) = 4x³ + 3x² + x – 14 b) f(x) =…

A: Solve derivative a fx=4x3+3x2+x-14b fx=4x-3+2x-4c fx=5ex-e3x

Q: Find the instantaneous rate of change for function at the given value. F(x) = x2 + 2 at x = 0

A: Given a function, F(x) = x2 + 2 at x = 0 To Find the instantaneous rate of change for function at…

Q: 4) f(x) e**+6x

A: If F(x) = f(g(x)) , then F'(x)= f'(g(x)).g'(x). dexdx=ex dxndx=n.xn-1. Quotient Rule of…

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

A: fx=x-1x+6

Q: Find f'(1) for f(x) = ln(3x² – 6x – 2) rounded to 3 decimal places. f'(1) = |6-6x/3x^2-6x-2

A:

Q: find f'(x) of (((3x^2+1)e^x^2)/(2x+1)^5)^5 using logaithmic differentiation.

A: The given function is,

Q: Find the local and absolute extremum for the functions over their domain: x²+2x-3 4. f(x) : x-2 ||

A:

Q: Find the domain of the function. f(x) = ln ( 1/ (x + 1)

A: f(x)=ln1x+1

Q: The demand for butter in Mexico for a particular year can be estimated by the general functionln q =…

A: lnq=D-0.47lnp Differentiating with respect to p, we get…

Q: Suppose that a room containing 1500 cubic feet of air is originally free of carbon monoxide.…

A:

Q: Use this formula to find the instantaneous rate of change of the function at the given x-value.f(x)…

A: Given function is

Q: 2x+4 f(x) = (3x + 7) e.

A: Given query is to find the derivative of f(x).

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

A:

Q: Consider the function f (x) = x2. Calculate the rate of change of f (x) at x = 1, and compare your…

A: Consider the function f (x) = x2  To Calculate the rate of change of f (x) at x = 1.

Q: The rate of growth of a population P is given by dP/dt=kP + N  where N is a constant representing…

A: Given:- The rate of growth of a population P is given by dP/dt=kP + N where N is a constant…

Q: Suppose f(x)=(x−3)/(x+4) Write an expression in terms of x and h that represents the average rate of…

A: fx=x-3x+4 The average rate of change of f over any interval x, x+h is fx+h-fxh.

Q: Find the equation of the secant line for f(x) = log2 (3x² + 2x – 1) from x = 1 to x = 3.

A:

Q: Find the derivative of the function g(x)=(5x^2−3x+1)e^x g'(x)=___

A:

Q: Differentiate. f(x) = - 2 e -X t'(x) = ]

A:

Q: Find the given higher-order derivative. F(3)(x) = Vx², f(4)(x) f(4)(x) =

A: Given that, the higher order derivative f(3)(x) = x23 To find the higher order derivative of f(4)(x)…

Q: Find the instantaneous rate of change of the function at the specified value of x. f(x)=(x−3)/(x+5)…

A: Given data:     The given function is: f(x)=(x-3)/(x-5).   The expression for the rate change of the…

Q: Find the domain of the function g(x) = /1 – x ln x

A: We have to find domain

Q: e) What are the domain and the range for this situation?

A:

Q: Let f(x) = (x² + 3x)e*. Determine the value of the third derivative of f(x) for x = 0.

A:

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

A:

Q: Find a real number a such that the instantaneous rate of change of the function flx) =2x²+ 4x+7 at x…

A:

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

A: Given       y = ln(x + 7)

Q: Suppose f(x)=(x−4)/(x+4). Write an expression in terms of x and h that represents the average rate…

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

Q: The duration (time in hours) of dialysis required is modeled by the function y = In(1.5x + 0.5/9x² –…

A:

Q: Suppose we have a tank that contain 10 litres of water and 50 g of salt. The salt solution is…

A: given , tank that contain 10liters of water and 50 gram of salt .  so , initial concentration =>…

Q: Find the derivative of f( x ) = a° log (x + 7.5). f'(x) =

A: We have to solve

Q: Find the linearization of the function f(x)=ln(2x+3) at x=-1

A:

Q: It has been estimated that the total production of oil from a certain oil well is given by T(t) =…

A:

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 the derivative of the given function 4. g(x) = (4 – 9x²)3 5. h(x) x+5 = x2-9, 6. A(x) = v3x3 +…

A:

Q: A company determines that its total cost, in thousands of 3x rands, for producing x items is C =…

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

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the derivative of the given function 4. g(x) = (4 – 9x²)³ 3 5. h(x) x+5 = x2-9, 6. A(x) = v3x³…

A:

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 linearization of the function k(x) = ln(x) when x= 1 and use it to estimate ln(1.1).

A:

Q: Suppose that the yield (measured in kg/ ha) of an agricultural crop is represented by the function…

A: We need to find rate.

Q: find the instantaneous rate of change of the function at the given x-value. f(x)=x2 + 3x at x=4

A: f(x)= x2+3x  and x=4

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

A:

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

A:

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: The duration (time in hours) of dialysis required is modeled by the function y = In(1.5x + 0.5V9x2 –…

A:

Q: Given the function g(x)=x² −2x³ +1, a. Estimate the instantaneous rate of change at x = 1. b. Will…

A:

Q: 2. The instantaneous rate of change of g(x) is the same for every real value of x. What conclusion…

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.