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3 years ago

What is the vertex of the graph of the function f(x) = (x + 2)^2 − 3?

Mathematics

1 answer:

forsale [732]3 years ago

5 0

25 it should be the answer

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“encontrar la integral indefinida y verificar el resultado mediante derivación”

Oliga [24]

$I=\displaystyle\int\frac x{(1-x^2)^3}\,\mathrm dx$

Haz la sustitución:

$y=1-x^2\implies\mathrm dy=-2x\,\mathrm dx$

$\implies I=\displaystyle-\frac12\int\frac{\mathrm dy}{y^3}=\frac1{4y^2}+C=\frac1{4(1-x^2)^2}+C$

Para confirmar el resultado:

$\dfrac{\mathrm dI}{\mathrm dx}=\dfrac14\left(-\dfrac{2(-2x)}{(1-x^2)^3}\right)=\dfrac x{(1-x^2)^3}$

$I=\displaystyle\int\frac{x^2}{(1+x^3)^2}\,\mathrm dx$

Sustituye:

$y=1+x^3\implies\mathrm dy=3x^2\,\mathrm dx$

$\implies I=\displaystyle\frac13\int\frac{\mathrm dy}{y^2}=-\frac1{3y}+C=-\frac1{3(1+x^3)}+C$

(Te dejaré confirmar por ti mismo.)

$I=\displaystyle\int\frac x{\sqrt{1-x^2}}\,\mathrm dx$

Sustituye:

$y=1-x^2\implies\mathrm dy=-2x\,\mathrm dx$

$\implies I=\displaystyle-\frac12\int\frac{\mathrm dy}{\sqrt y}=-\frac12(2\sqrt y)+C=-\sqrt{1-x^2}+C$

$I=\displaystyle\int\left(1+\frac1t\right)^3\frac{\mathrm dt}{t^2}$

Sustituye:

$u=1+\dfrac1t\implies\mathrm du=-\dfrac{\mathrm dt}{t^2}$

$\implies I=-\displaystyle\int u^3\,\mathrm du=-\frac{u^4}4+C=-\frac{\left(1+\frac1t\right)^4}4+C$

Podemos hacer que esto se vea un poco mejor:

$\left(1+\dfrac1t\right)^4=\left(\dfrac{t+1}t\right)^4=\dfrac{(t+1)^4}{t^4}$

$\implies I=-\dfrac{(t+1)^4}{4t^4}+C$

4 0

3 years ago

The points at which the curve changes from curving upward to curving downward are called what

marshall27 [118]

Answer:

Inflection points. It's where the second derivative of the function is equal to zero

Step-by-step explanation:

7 0

3 years ago

In AOPQ , the measure of angle Q=90^ , OQ = 33, PO = 65 , and QP = 56 What ratio represents the tangent of angle P ?

ladessa [460]

Ahhhhhhhhhhhhhhhhhjjhhhhhh

4 0

3 years ago

Use the rules of exponents to evaluate and simplify the following expression. Type all without negative exponents. Do not distri

Rainbow [258]

We are given (xy)^(-3).

This leads to 1/(xy)^3.

You see, going from the top to the bottom alters the sign of the exponent to its opposite.

ANSWER: 1/(x^3•y^3)

Did you follow?

5 0

3 years ago

Use the unit circle to find the inverse function value in degrees.<br> tan^-1 sqrt 3

mr Goodwill [35]

Use the unit circle to find the inverse function value in degrees.tan^-1 sqrt 3

The correct answer would be 60 degrees. Since you are asked to find an angle that the tangent is equal to sqrt 3. The only angle that is equal to that given the interval is 60 degrees. So that is the correct answer. I hope this answer helped you.

7 0

3 years ago