Quiz about Derivate e integrali

Question 1

Una funzione si dice integrabile in senso proprio (a,b) se

Accepted Answer

continua in (a,b)

Answer

positiva

Answer

discontinua in (a,b)

Question 2

Calcola $$\int_0^1\ x\ dx$$

Accepted Answer

$$\frac{1}{2}$$

Answer

1

Answer

2

Answer

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

Question 3

derivata e integrale di $$f\left(x\right)=x$$

Accepted Answer

1

Accepted Answer

$$\frac{x^2}{2}+c$$

Answer

$$x^2$$

Answer

x

Question 4

Derivata di $$\sin\left(x\right)$$

Accepted Answer

$$\cos\left(x\right)$$

Answer

$$-\sin\left(x\right)$$

Answer

$$-\cos(x)$$

Question 5

primitiva di $$-\cos\left(x\right)$$

Accepted Answer

$$-\sin\left(x\right)$$

Answer

$$\sin\left(x\right)$$

Answer

$$\cos\left(x\right)$$

Question 6

$$\frac{d}{dy}\left(x^2+y\right)$$ =

Accepted Answer

$$x^2+1$$

Answer

$$x^2+y^2$$

Answer

$$2x+y$$

Question 7

se f(x) polinomio di secondo grado allora $$f$$ =

Accepted Answer

0

Answer

$$f\left(x$$

Answer

1

Answer

$$F$$

Question 8

$$\left(e^x\right)$$ =

Accepted Answer

$$e^x$$

Answer

$$e$$

Answer

$$xe^x$$

Answer

$$\frac{e^x}{x}$$

Question 9

la formula del rapporto incrementale di una qualsiasi funzione derivabile

Accepted Answer

$$\lim_{h\rightarrow0^+}\frac{f\left(x\right)-f\left(x+h\right)}{h}$$

Answer

$$\lim_{h\rightarrow0^+}\frac{f\left(x\right)-f\left(x+h\right)}{x+h}$$

Answer

$$\lim_{h\rightarrow0^-}\frac{f\left(x\right)-f\left(x+h\right)}{h}$$

Answer

$$\lim_{h\rightarrow0^+}\frac{f\left(x\right)+f\left(x-h\right)}{h}$$

Question 10

Un integrale indefinito si dice convergente se

Accepted Answer

$$f\left(x\right)\le\frac{1}{x^2}$$ definitivamente

Answer

$$\lim_{x\rightarrow\infty}f\left(x\right)=0$$

Answer

$$\lim_{x\rightarrow\infty}f\left(x\right)\in R$$

Question 11

$$\int_{ }^{ }x+1\ dx=$$

Accepted Answer

$$\frac{x^2}{2}+x+c$$

Answer

$$x^2+x$$

Answer

$$x^2+c$$

Answer

$$\frac{x}{2}+c$$

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