Quiz about Cálculo Diferencial (Capítulos 3,4,5)

Question 1

La pendiente de una recta paralela al eje $$x$$ es:

Accepted Answer

0

Answer

1

Answer

-1

Answer

Positiva

Question 2

Si $$\frac{\Delta y}{\Delta x}=3x^2+3x\Delta x+\left(\Delta x\right)^2-1$$ para $$y=f\left(x\right)=x^3-x+2$$ entonces $$f$$

Accepted Answer

$$\lim_{\Delta x\rightarrow0}\left(3x^2-1\right)$$

Answer

$$3x^2$$

Answer

$$\lim_{\Delta x\rightarrow0}3x^2$$

Answer

$$3x$$

Question 3

Sea $$y=3x^2+4$$ . Se cumple que $$\frac{\Delta y\ }{\Delta x}=$$

Accepted Answer

$$6x+3\Delta x$$

Answer

$$6x$$

Answer

$$3x^2+\Delta x$$

Answer

$$6x\Delta x\ $$

Question 4

Si $$c$$ es una constante y $$u=f\left(x\right)$$ entonces $$\frac{d}{dx}\left(cu\right)=$$

Accepted Answer

$$c\ \frac{du}{dx}$$

Answer

$$\left(\frac{du}{dx}\right)^c$$

Answer

$$u\ \frac{dc}{dx}$$

Answer

$$\frac{1}{c}\frac{du}{dx}$$

Question 5

Si $$u=f\left(x\right)$$ entonces $$\frac{d}{dx}\left(\sqrt{u}\right)=$$

Accepted Answer

$$\frac{1}{2\sqrt{u}}\frac{du}{dx}$$

Answer

$$\frac{1}{2\sqrt{u}}$$

Answer

$$-\frac{1}{2\sqrt{u}}$$

Answer

$$2u^{-\frac{1}{2}}\frac{du}{dx}$$

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