A certain bacterial culture grows at a rate proportional to the number of bacteria present. If the culture contains 400 cells initially and 700 after 24 hours, then approximately how many cells will there be after a further 12 hours?

Q: The limit represents f '(c) for a function f(x) and a number c. Find f(x) and c. 4√5-4 f(x) C = =…

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Q: Determine the point(s) at which the given function f(x) is continuous. 9. x-9 f(x)= -2x Describe the…

A: We can find the answer in the below steps.

Q: For f(x)=x2+4 and g(x)=x2-4 find the following function (gof)(x)

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Q: 3x² - y2 + 18x-2y-10=0 4x²-4y²-8x-8y-19 = 0

A: Given Equations:- 1. 3x2-y2+18x-2y-10=0 2. 4x2-4y2-8x-8y-19=0

Q: Determine 1) a₁ = -3, r=4 if each geometric series converges or dive 3) a₁ = 5.5, r=0.5 5) 81…

A: Solution

Q: Evaluate the following integral for some constants 1 ‡ a > 0 and b. a. b. C. a-1 ab ln a 1-a ab In a…

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Q: 5.  Determine whether the improper integral converges and, if so, evaluate it.   ∞ 0 5x dx (3 +…

A: Please see the below picture for detailed solution.

Q: [t² sin ßt dt, where 3 is a constant

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Q: Calculate the derivative. (Use symbolic notation and fractions where needed.) d dy (4y³ + 15y4/5) =

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Q: Q4/ The population of Baghdad in 2010 was 5652000. If the population in 2020 was 7144000, find the…

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Q: A population, P(t) (in millions) in year t, increases exponentially. Suppose P(8) = 22 and P(15) =…

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Q: Use trigonometric substitutions to evaluate the definite integral 1 [5x²³√1-x² dx.

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Q: y = (ex-e-x) (ex+e-x)

A: To find the derivative

Q: A large die-casting machine used to make automobile engine blocks is purchased for $2.5 million. For…

A: This question can be solved using the equationV=Vo(1-R)n   WhereV=value of the machine after n…

Q: QUESTION 12 A ball is thrown into the air. Its height in feet seconds later is given by y=40t -…

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Q: 5. Find a parameterization for the intersection of a) the cylinder x² + y² = 9 and the plane z = = 2

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Q: velocity speed f(t) = 85t - 5t² I m/s m/s

A: Given; f(t)=85t-5t2, t=3.

Q: Question Given f(x) = -4x³ – 3, use a table to estimate the slope of the tangent line to f at the…

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Q: car is parked 55 feet from a long warehouse (see figure). The revolving light on top of the car…

A: Solution: Given A car is parked 55 feet from a long warehouse. The revolving light on the top of the…

Q: Find the length of the curve. r(t) = cosíti + sinét j – 4´t k, 0≤t≤2

A: I have appended the formula used in the solution part of the question

Q: Find dy/dx and d2y/dx2 at the given point without eliminating the parameter x = θ + cos θ, y = 1 +…

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Q: For f(x)= square root x and g(x)=x-1 find the following function (fog)(x) I=

A: To find the (fog)(x)

Q: Fencing a Field Consider the following problem: A farmer has 2400 ft of fencing and wants to fence…

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Q: Find f + g, f − g, fg, and f/g and their domains. f(x) = x,    g(x) = 5x

A: Given  f(x) = x  and  g(x) = 5x.

Q: Then Graph, emphasize the Limit. 5. lim x-3 √²-5+2 x-3

A: limx→3x2-5+2x-3 We have to find the limit.

Q: Verify that the given point is on the curve. Find the lines that are a. tangent and b. normal to the…

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Q: Compute the integral (a) sin(x) dx by letting u = x. (b) e/2dx by letting u = x/2. Show that you got…

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Q: Find the second derivative of ƒ(x) if ƒ(x) = (5x+3)³.

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Q: The graph of f(x) is shown below. Which of the following statements are true? 8 7 60 5 4 3 2 1 M -8…

A: Ax x=6, limx→6-f(x)=limx→6+f(x)=f(6)

Q: Suppose that lim f(x) = 9 and lim g(x) = -5. Find the following limits. X-4 X-4 a. lim [f(x)g(x)]…

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Q: In R TOHE R² 1 √√3 J₁ 1 dR arctan(1/x)dx

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Q: The function f(x) = x³ + 5x²-√x + 1 is a polynomial of degree 3.

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Q: O In(e) O In(2) Ove Oe² What is ef'(2) if f(x) = In(x)?

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Q: Calculate the derivative. (Use symbolic notation and fractions where needed.) d dx (-9x³ + 4x² - 7x)…

A: Topic - derivative of a function. we are given function:-9x3+4x2-7xand we know thatddxxn=nxn-1

Q: Given that lim f(x) = 4 X-1 (b) lim [g(x)]³ X-1 (c) lim x-1 find each limit, if it exists. (If an…

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Q: What is the equation of the tangent line to f(x)=3e²x+cos4x at x = 0?

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Q: Set up but do not evaluate the integral to find the length of the arc of the curvey = x = 5 to x =…

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Q: y = 25x . 32x

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Q: Find the area of the triangle PQR

A: As we know that; If the vertices of the triangle△PQR are given, then the expression for the area of…

Q: Question Given f(x) = 2 - 5x³, use a table to estimate the slope of the tangent line to f at the…

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Q: f(x)=square root x+7, g(x)=square root x-5 Find f-g and then determine the domain for the function

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Q: Let F(x) = f(g(x)), , where f(-7)=2, f'(-7) = 3, f'(3) = 10, g(3) = −7, and g'(3) = -9, find F'(3) =

A: Given, F(x)=f(g(x)),

Q: go O II 6 Paragraph For f(x)= x2+4 and g(x)=x2-4 find the following function (gof)(2) HE 7 Ty F8 G…

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Q: Question Find the points at which the following function is discontinuous. 6x²+1 f(x) = -5x -5 if x…

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Q: 4-Evaluate sin-1 (-¹).

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Q: If f(x)= 3x +41, which of the following is true? Select one: O a. f is not continuous but is…

A: Let's find function is continuous and differential at given point.

Q: Fencing a Field Consider the following problem: A farmer has 2400 ft of fencing and wants to fence…

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Q: Suppose a disease is introduced to a population of fruit flies and the population of flies decreases…

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Q: Find the partial traction decomposition of p(2) (2) p(a)=-5212+10511-490 10-1763 +5778 +230427+58852…

A: We have to find p(x)/q(x).

Q: For the function f(x) given in the table, find the average rate of change over each specified…

A: For the function f(x)  given in the table, find the average rate of change over each specified…