For the function g(x)=10 ^(x-3) -2, determine the effects the transformation has on the domain and range of the parent function f(x)=10^x.

Q: Find the derivative.   g(x) = 4^x/x^4

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Q: of tax returns that will be electronically filed for 2010 using exponential smoothing with α=0.1

A: Solution

Q: A point is moving on the graph of y³ = x². When the point is at (-512, 64), its y coordinate is…

A: Given, A point is moving on the graph of  y3 = x2. When the point is at -512, 64, its y coordinate…

Q: Suppose that a liquid carries a drug with concentration 0.1 g/cc into a 300-cc organ at a rate of 5…

A: Given: the concentration of the drug carried by  the liquid=0.1g/cc liquid enters and leaves the…

Q: The Loth Cat population grows at a constant relative growth rate. If the population is 400 after 2…

A: Let the constant relative growth rate be 'r' and the time in years be 't'. Let the population at any…

Q: Suppose that you can calculate the derivative of a function using the formula f′(x)=3f(x)+1x. If the…

A: Derivative of a function using the formula f′(x)=3f(x)+1x and f(3)=6. We know that approximate…

Q: Find the maximum rate of change of f at the point (1, 2). -2/2 2/2 4 -4

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Q: Can you help me find the derivative of f(x)=x8(x4- 6/x4) (this needs to be solved without using the…

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Q: Find the third derivative of y = (6x - 1). Show your %3D in negative exponent.

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Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: The given function of production cost is To find average rate of change of total cost ,use formula

Q: Suppose that you can calculate the derivative of a function using the formula f′(x)=5f(x)+3x. If the…

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Q: Describe the Chain Rule for the composition of two differentiable functions in your own words.

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Q: Find the derivative off(x)=−5x^8+8x^4 f'(x)=______

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Q: x+1

A: By using the formula you can solve the given problem as follows :

Q: The worst ecological disaster in U.S. history began on April 20, 2010, and was caused by an…

A: bn=2.520n & rn=441,000n a). an=bn-rn=2.520n-441,000n=-4,40,997.48n

Q: se the chain rule to find the derivative of f(x)=4√2x3+7x8 Type your answer without fractional or…

A: given f(x)=4√2x3+7x8 f'(x) = dfdx        =d42x3+7x8dxwktda+bdx = dadx+dbdx

Q: Find the derivative of f(x) = x + 4". f'(x) = %3D

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Q: Find the First derivative of 5x/2 4x %3D

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Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: Given,         The total cost in dollars from the production of x printers is given by…

Q: Find the derivative of f (x) = (5 – 3x)2. %3D

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Q: Suppose that the daily profit (in dollars) from the production and sale of x units of a product is…

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Q: Explain why the derivative of x2 + y2 + 2 = 1 does not mean anything.

A: x2+y2+2=1 On simplification, we get ⇒x2+y2=1-2⇒x2+y2=-1 This curve does not exist as the sum of two…

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: Suppose total cost in dollar from the production of x printers is given byC(x) =…

Q: Find the derivative. g(x) = (4x – 2)° – Vr + 8

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Q: A cigar manufacturer produces x cases of cigars per day at a daily cost of 50x(x + 200)>(x + 100)…

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Q: Find the derivative of the inverse of the function f(x)=x* – 5x² +1, for 0<x<2, at the point (-3,1)…

A: To find the derivative of the inverse of the function f(x)=x4-5x3+1 at a point (-3,1), where (-3,1)…

Q: Answer fast. Find the 5th derivative of 3x^5 - 3x^3 + (1 /x^2).

A: We differentiating with respect to x continuously 5 times to get the required 5th derivative.

Q: The half-life of radium-226 is 1590 years. (a) If a sample has a mass of 150 mg, find a function…

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Q: The demand for a natural resource t years from now will be increasing at a rate of te0.0017 million…

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Q: Estimate the instantaneous rate of change of f(x) = -3x + 2 at x = -2.

A: The instantaneous rate of change of a function f(x) is the first derivative of a given function and…

Q: Find the derivative of f (x) = (x – 4) / 10x³ + 1. -

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Q: Find the derivative of (x-x^4)/(7/x^2+6/x^3)

A: Formula used:

Q: Find the instantaneous rate of change for the function: f (x)= 4x = 2x²- 5

A: The instantaneous rate of change of function will be find by differentiate the function with respect…

Q: Suppose the percent of males who enrolled in college within 12 months of high school graduation is…

A: Given:         Percent of males enrolled in college is    y= -0.126x + 55.72         Percent of…

Q: What is the instantaneous rate of change of the function f ( x ) = 5 /x  at x = 3 ?

A: Given,        The instantaneous rate of change of the function fx=5x at x=3.We know that,…

Q: Suppose that the daily profit (in dollars) from the production and sale of x units of a product is…

A: x is the number of units produced and sold. The Profit function is given by P = 150x − x^2/500−…

Q: Find the second derivative of f(x)=x(x^2+1)^3

A: Find the derivative of function:

Q: Find the derivative of the logarithmic function. f(x) = 2x² In 2x f'(x)= 4in (2x) + 6

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Q: Answer fast. Find the 5th derivative of 3x^5 - Зx^3 + (1 /x^2).

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Q: y = ln (7x³ + 5)* 4

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Q: What is the equation for the transformed function? While using f(x)

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Q: Suppose that the daily profit (in dollars) from the production and sale of x units of a product is…

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Q: What is the derivative of y=(1-x-1)-1  Please show steps. Thanks.

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Q: Find the second derivative of f(x)=x^3 + x-5

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Q: 14x

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Q: A money market fund has a continuous flow of money at a rate of f(x)=1500x-170x2 for 10 years. Find…

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Q: Find the derivative of f (x) 2x5 9x f'(x) =

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Q: Find the first and second derivative if y=4-2x-x-3

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.