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3 years ago

PLEASE HELP ME WITH THIS MATH QUESTION ASAP!!

Mathematics

1 answer:

kirza4 [7]3 years ago

3 0

Answer:

f(x) = 2x+3

g(x) = 1/x^2

Step-by-step explanation:

There are many ways you can write the given expression as a function of a function. In general, you want to think about the operations that are performed on the variable, then consider which operations might be performed first, and what operations might be performed on the results of the first ones.

When the given expression is evaluated, you ...

• square the variable

• divide 2 by the result

• add 3 to that result

It is reasonable to divide this list into two parts, then make one function do one part of the list and the other function do the other part.

In our selection of f() and g() above, we have chosen to make g(x) be ...

• square the variable

• find the reciprocal of that result

and we have defined f(x) to be

• multiply that result by 2

• add 3.

You will note that multiplying the reciprocal by 2 is the same as dividing 2 by the result.

_____

Our f(x) and g(x) are ...

g(x) = 1/x^2

f(x) = 2x +3

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3 years ago

A. Evaluate ∫20 tan 2x sec^2 2x dx using the substitution u = tan 2x.

irakobra [83]

Answer:

The integral is equal to $5\sec^2(2x)+C$ for an arbitrary constant C.

Step-by-step explanation:

a) If $u=\tan(2x)$ then $du=2\sec^2(2x)dx$ so the integral becomes $\int 20\tan(2x)\sec^2(2x)dx=\int 10\tan(2x) (2\sec^2(2x))dx=\int 10udu=\frac{u^2}{2}+C=10(\int udu)=10(\frac{u^2}{2}+C)=5\tan^2(2x)+C$ . (the constant of integration is actually 5C, but this doesn't affect the result when taking derivatives, so we still denote it by C)

b) In this case $u=\sec(2x)$ hence $du=2\tan(2x)\sec(2x)dx$ . We rewrite the integral as $\int 20\tan(2x)\sec^2(2x)dx=\int 10\sec(2x) (2\tan(2x)\sec(2x))dx=\int 10udu=5\frac{u^2}{2}+C=5\sec^2(2x)+C$ .

c) We use the trigonometric identity $\tan(2x)^2+1=\sec(2x)^2$ is part b). The value of the integral is $5\sec^2(2x)+C=5(\tan^2(2x)+1)+C=5\tan^2(2x)+5+C=5\tan^2(2x)+C$ . which coincides with part a)

Note that we just replaced 5+C by C. This is because we are asked for an indefinite integral. Each value of C defines a unique antiderivative, but we are not interested in specific values of C as this integral is the family of all antiderivatives. Part a) and b) don't coincide for specific values of C (they would if we were working with a definite integral), but they do represent the same family of functions.

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3 years ago

What is 1(z) when z = -7/12

Firlakuza [10]

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2 years ago

Read 2 more answers

What is the value of x in the equation <br> -5/8x=-160?

Helen [10]

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