Q: f(x + 1) ,find f(x – 2) f (x) = 27x
A: Given that, fx=3x27x Evaluate: fx+1fx-2
Q: Find the relative extrema of f(x) = (x4 + 1)/x2 .
A: Given: f(x) = (x4 + 1)/x2 To Find: Relative extrema of f(x). Concept: First-Derivative Test:
Q: Given the function f(x) = Vx5 – 3Vx2, find the interval(s) of increase.
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Q: Find f'(x) for f(x) = e5a+2x
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Q: Find f' (a) for 13x f(x) = 9x + 8 f' (a) =
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Q: Find the relative extrema of f (x) = 3x5 – 5x3 %3D
A: To find The relative extremum of f(x).
Q: Find the antiderivative of f(x) = x³ – 6x +7
A: fx=x3-6x+7 to find the antiderivative, we need to take an integration Fx=∫ fxdx
Q: (d) f(x) = ev4r+1 f'(x) = ,
A:
Q: If f(x) dx = 4x7 – 6x5 + C, find f(x). %3D -
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Q: For f(x) = 2x² + 5x+", find. 10 S(a +h)- f(a) if h +0. h
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Q: If f(x) = 5x¹(²), find ƒ'(6) to 3 decimal places.
A: The given function, f(x)=5xlnx
Q: If f(x)=∫8/x t^2dt f'(x)=?
A: As per fundamental rule II of calculus, the releationship is as shown on the white board.
Q: Find the extreme values of f(x, y) = x² .
A: Given, f(x, y)=x2+2y2 ...(1) Subject to…
Q: What is the domain of f (x) = ln(x – 3) + 4?
A: Domain where fx is well defined.
Q: Find the relative extrema. x2 f(x) = 16- — х2
A: Given: f(x)=x216−x2 Function achieves relative maximum or relative minimum (relative extrema) at…
Q: x2 - 2x + 1
A: The expression to calculate the the antiderivative of the given function: Fx=∫fxdx The Power rule:…
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Q: If f(x) = ln ( v3x² +5 ), what is f'(x)?
A:
Q: If f(x) dx = 37 and g(x) dx = 12, find [4f(x) + 5g(x)] dx. %3D
A: Given : ∫06fxdx = 37∫06gxdx = 12
Q: Find [f(x) + 5g(x)]dx if 6. f(x)dx = 4 and g(x)dx = -5. juo 6. f(x) + 5g(x)]dx -3
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Q: if f(x) = 3x+4 over 4x+3 then f'(x)=?
A: Given: fx=3x+44x+3 To Find: f'x=?
Q: Differentiate. xex - f(x) x + eX x². e* + e2x + 8 + 8e* f '(x) = (x+ e*)? 2
A:
Q: What is the domain of y=ln(x^2+3x−18)
A: Consider the given function
Q: If f(x) = 4x² ln(7x), then %3D f'(x) = f" (x) = f" (x) =
A: The given function is: f(x)=4x2ln(7x) so, f'(x)=4x2ddx(ln(7x))+ln(7x)ddx(4x2)…
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Q: Find the antiderivative of f(x)=x3−6x+7
A: Given: f(x)=x3-6x+7
Q: Find the most general antiderivative of f(æ) = -5x + (1 – a²)-1/2, where -1 < x < 1. F(x) =
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Q: f (x) = 3.x5 5x3.
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Q: Find the antiderivative of f(x) f(x)=2sec2 (x)-3x-6
A: Given: f(x)=2sec2x-3x-6let the antiderivative of f(x) = F(x)then,F(x)=∫f(x)dx
Q: If f(x) = 5x4-2x³-x²+3x - 1, then | f'(0) = %3D d2 f(0) = dx f"(x)= d4 dx 4
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Q: Find f'(x) for f (x) = v5+ e2x
A: Given, fx=5+e2x
Q: Comput: f dx 2+x
A: I am attaching image so that you understand each and every step.
Q: Plot f (x) = x e - x and use the zoom feature to find two solutions of f (x) = 0.3.
A: Using a graphing calculator we plot f(x)
Q: Find the approximate value of f (3.02), where f(x) = 3x2 + 5x + 3.
A: Given
Q: If f(x) dx о = 39 and д(x) dx 16, find [3f(x)5g(x)] dx.
A: The given values of integrals are,
Q: Find f '(a) for f(x) = 3 − 2x + 4x2
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Q: f(x) = (x² – 2x + 2)e*
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Q: With f(x) = 3x +1 and h(x) = 2x – 4, find (f o h)(5)
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Q: If f(2) = 11, f' is continuous, and f "(x) dx = 18, what is the value of f(4)? f(4) =
A: Solve the given problem.
Q: Given the revenue function R(x) = x³ + 3x2 +x .Find the average revenue of producing 100 units. %3D
A: Given the revenue function, R(x), the average revenue of producing 100 units is R(100)100
Q: Find the extreme values of f(x, y) = x² + y² .
A: The given function is f(x,y)=x2+y2. Find the extreme values of f(x,y)=x2+y2 as follows.
Q: Find the value of x and y for f(x)=3x2+9xy-y2-9x,if fx(x,y)=0 and fy(x,y)=0
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Q: What is f'(x) of the function f(x) = 4xy^3 if you consider y as a constant?
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Q: z² – 4x + 4 Differentiate f(x)
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Q: Find the most general antiderivative of the function f(x) = 72° – 6x³ + 3x?.
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Q: If f(x) dx 39 and g(x) dx = 12, find [2f(x) + 3g(x)] dx. %3D
A:
Q: Find f'(x). 12x f(x) = e f'(x) =D %3D
A:
Q: Find f(0) iff (x) et?
A:
Q: 1 f(x) = x²- 4x %3D
A:
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Two different types of polishing solutions are being evaluated for possible use in a tumble-polish operation for manufacturing interocular lenses used in the human eye following cataract surgery. Three hundred lenses were tumble polished using the first polishing solution, and ofthis number, 253 had no polishing-induced defects. Another 300 lenses were tumble-polishedusing the second polishing solution, and 196 lenses were satisfactory upon completion.(a) Is there any reason to believe that the two polishing solutions differ? Use α = 0.01First Order Linear DE and Bernoulli DE
- The iHub features an array of 3D printers for student use. 3D printers use plastic filament spools to print out plastic parts. The iHub purchases 85% of their filament spools from Amazon, and the rest of their filament spools from Flash Forge. It has been determined that 9% of the filament spools from Amazon are defective, while only 3% of the filament spools from Flash Forge are defective. i) The iHub randomly selects one filament spool from its inventory. What is the probability of it being a defective filament spool? (three decimals) ii) If a filament spool at the iHub is randomly selected and determined to be defective, what is the probability that the filament spool was purchased from Amazon? (three decimals)In winter of a country, it rains 45% of the days and shine 55% of the days. Mr. X has abarometer which wrongly predicts 5% of the time in rainy days and 10% on shiny days.Mr. X does not carry umbrella if barometer predicts shine. On good shiny morning inwinter, his barometer predicts “shine” and he does not carry umbrella. What is theprobability that Mr. X will suffer from rain on that day.In the construction process for solid-state flash memory drives (thumb drives), nearly all drives areconstructed with a large potential amount of storage space, and are sold base on the actual amountof memory that forms correctly during the process (For example, drives that are designed to store 64gb but contain a large number of bad sectors will instead be formated and sold as 32 gb). Consider amanufacturing process where every chip has a 21% of having enough bad sectors to be downgraded,and these errors are random and independent.(a) If we wish to compute the probability thatxnumber of chips out of a production run of sizenaredowngraded, do we have a probability distribution that will work for that? Are the assumptionsfor that met? Explain. (b) Compute the probability that 5 chips out of a production run of 40 are downgraded. (c) Compute the probability that between 3 and 5 (inclusive)orbetween 2 and 8 (inclusive) aredowngraded. (d) Graph the probability mass function forxnumber of…
- In the construction process for solid-state flash memory drives (thumb drives), nearly all drives areconstructed with a large potential amount of storage space, and are sold base on the actual amountof memory that forms correctly during the process (For example, drives that are designed to store 64gb but contain a large number of bad sectors will instead be formated and sold as 32 gb). Consider amanufacturing process where every chip has a 21% of having enough bad sectors to be downgraded,and these errors are random and independent. (a) If we wish to compute the probability that x number of chips out of a production run of size n are downgraded, do we have a probability distribution that will work for that? Are the assumptionsfor that met? Explain. (b) Compute the probability that between 3 and 5 (inclusive)or between 2 and 8 (inclusive) are downgraded. (c) Graph the probability mass function for x number of chips out of a production run of 10 aredowngraded.Here are the choices: >The defective/nondefective classification depends on machinist classification >10.88 >Failed to reject the null >11.2 >2 >The defective/nondefective classification is independent on machinist classification >Reject the null >3X-Linked Genetic Disease Men have XY (or YX) chromosomes and women have XX chromosomes. X-linked recessive genetic diseases (such as juvenile retinoschisis) occur when there is a defective X chromosome that occurs without a paired X chromosome that is good. In the following, represent a defective X chromosome with lowercase x, so a child with the xY or Yx pair of chromosomes will have the disease and a child with XX or XY or YX or xX or Xx will not have the disease. Each parent contributes one of the chromosomes to the child. a. If a father has the defective x chromosome and the mother has good XX chromosomes, what is the probability that a son will inherit the disease? b. If a father has the defective x chromosome and the mother has good XX chromosomes, what is the probability that a daughter will inherit the disease? c. If a mother has one defective x chromosome and one good X chromosome and the father has good XY chromosomes, what is the probability that a son will inherit the…
- In a class of 40 students 25 speaks hindi and 15 speaks both english and hindi. All students speak atleast onr of the two languages . How many speak only englishI am having troble interpreting these two tables.You rolled a six-sided die 60 times and got the following tallly 20 ones. 20 twos. 15 threes. 3 fours. 2 fives. 0 sixes. Does this seem like a reasonable result? What interference might you draw from the result?