Quiz about Inverse D-operator (part 1)

Question 1

Which inverse D-operator formula is used to compute $$\frac{1}{D^2}\left(5\right)$$ ?

Accepted Answer

$$\frac{1}{D}\left[f\left(x\right)\right]=\int f\left(x\right)\ dx$$

Answer

$$\frac{1}{F\left(D\right)}\left(k\right)=\frac{1}{F\left(0\right)}\cdot k$$

Answer

$$\frac{1}{F\left(D\right)}\left[e^{kx}\right]=\frac{1}{F\left(k\right)}\cdot e^{kx}$$

Answer

$$\frac{1}{F\left(D\right)}\left(k\right)=\frac{1}{F\left(k\right)}\cdot k$$

Question 2

Which inverse D-operator formula is used to compute $$\frac{1}{D^2-1}\left(5\right)$$ ?

Accepted Answer

$$\frac{1}{F\left(D\right)}\left(k\right)=\frac{1}{F\left(0\right)}\cdot k$$

Answer

$$\frac{1}{D}\left[f\left(x\right)\right]=\int f\left(x\right)\ dx$$

Answer

$$\frac{1}{F\left(D\right)}\left[e^{kx}\right]=\frac{1}{F\left(k\right)}\cdot e^{kx}$$

Answer

$$\frac{1}{F\left(D\right)}\left(k\right)=\frac{1}{F\left(k\right)}\cdot k$$

Question 3

What does it mean by the formula $$\frac{1}{F\left(D\right)}\left(k\right)=\frac{1}{F\left(0\right)}\cdot k$$ ?

Accepted Answer

replace all D by 0

Answer

replace all k by 0

Answer

replace all D by k

Answer

multiply F by 0

Question 4

Which inverse D-operator formula is used to compute $$\frac{1}{D^2-1}\left(e^{2x}\right)$$ ?

Accepted Answer

$$\frac{1}{F\left(D\right)}\left[e^{kx}V\left(x\right)\right]=e^{kx}\cdot\frac{1}{F\left(D+k\right)}\left[V\left(x\right)\right]$$

Accepted Answer

$$\frac{1}{F\left(D\right)}\left[e^{kx}\right]=\frac{1}{F\left(k\right)}\cdot e^{kx}$$

Answer

$$\frac{1}{F\left(D\right)}\left(k\right)=\frac{1}{F\left(0\right)}\cdot k$$

Answer

$$\frac{1}{F\left(D\right)}\left(k\right)=\frac{1}{F\left(k\right)}\cdot k$$

Question 5

What does it mean by the formula $$\frac{1}{F\left(D\right)}\left[e^{kx}\right]=\frac{1}{F\left(k\right)}\cdot e^{kx}$$ ?

Accepted Answer

replace all D by k

Answer

replace all D by 0

Answer

replace all k by 0

Answer

multiply all D by k

Question 6

Which inverse D-operator formula is used to compute $$\frac{1}{D^2-1}\left(e^x\right)$$ ?

Accepted Answer

$$\frac{1}{F\left(D\right)}\left[e^{kx}V\left(x\right)\right]=e^{kx}\cdot\frac{1}{F\left(D+k\right)}\left[V\left(x\right)\right]$$

Answer

$$\frac{1}{F\left(D\right)}\left(k\right)=\frac{1}{F\left(0\right)}\cdot k$$

Answer

$$\frac{1}{F\left(D\right)}\left[e^{kx}\right]=\frac{1}{F\left(k\right)}\cdot e^{kx}$$

Answer

$$\frac{1}{F\left(D\right)}\left(k\right)=\frac{1}{F\left(k\right)}\cdot k$$

Question 7

What does it mean by the formula $$\frac{1}{F\left(D\right)}\left[e^{kx}\ V\left(x\right)\right]=e^{kx}\cdot\frac{1}{F\left(D+k\right)}\left[V\left(x\right)\right]$$ ?

Accepted Answer

put $$e^{kx}$$ outside the operator and replace all D by (D+k)

Answer

replace all D by (D+k)

Answer

put $$e^{kx}$$ outside the operator and add $$F\left(D\right)$$ by k

Answer

replace $$F\left(D\right)$$ by k

Question 8

Which inverse D-operator formula is used to compute $$\frac{1}{D^2-1}\left(\sin x\right)$$ ?

Accepted Answer

$$\frac{1}{F\left(D^2\right)}\left[\sin kx\right]=\frac{1}{F\left(-k^2\right)}\cdot\sin kx$$

Answer

$$\frac{1}{F\left(D\right)}\left(\sin x\right)=\frac{1}{F\left(0\right)}\cdot\sin x$$

Answer

$$\frac{1}{D^2+k^2}\left[\sin kx\right]=-\frac{x\ \cos kx}{2k}$$

Answer

$$\frac{1}{F\left(D\right)}\left(\sin kx\right)=\frac{1}{F\left(k\right)}\cdot\sin kx$$

Question 9

What does it mean by the formula $$\frac{1}{F\left(D^2\right)}\left[\sin kx\right]=\frac{1}{F\left(-k^2\right)}\cdot\sin kx$$ ?

Accepted Answer

replace all $$D^2$$ by $$-k^2$$

Answer

replace all D by $$-k^2$$

Answer

replace all D by $$-k$$

Answer

replace all $$D^2$$ by $$k^2$$

Question 10

Which inverse D-operator formula is used to compute $$\frac{1}{D^2+1}\left(\sin x\right)$$ ?

Accepted Answer

$$\frac{1}{D^2+k^2}\left[\sin kx\right]=-\frac{x\ \cos kx}{2k}$$

Answer

$$\frac{1}{F\left(D\right)}\left(\sin x\right)=\frac{1}{F\left(0\right)}\cdot\sin x$$

Answer

$$\frac{1}{F\left(D^2\right)}\left[\sin kx\right]=\frac{1}{F\left(-k^2\right)}\cdot\sin kx$$

Answer

$$\frac{1}{F\left(D\right)}\left(\sin kx\right)=\frac{1}{F\left(k\right)}\cdot\sin kx$$

Inverse D-operator (part 1)

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