Evaluate the expression for the value of x=-3. (If not possible, state the reason)<br><br> 2x-2

Find the given derivative by finding the first few derivatives and observing the pattern that occurs. d103 dx103 (sin(x))

aleksandrvk [35]

To find $\frac{d^{103}}{dx^{103}} \left(\sin{(x)}\right)$ , we find the first few derivatives and observe the pattern that occurs.

$\frac{d}{dx} (\sin{(x)})=\cos{(x)} \\ \\ \frac{d^2}{dx^2} (\sin{(x)})= \frac{d}{dx} (\cos{(x)})=-\sin{(x)} \\ \\ \frac{d^3}{dx^3} (\sin{(x)})= -\frac{d}{dx} (\sin{(x)})=-\cos{(x)} \\ \\ \frac{d^4}{dx^4} (\sin{(x)})= -\frac{d}{dx} (\cos{(x)})=-(-\sin{(x)})=\sin{(x)} \\ \\ \frac{d^5}{dx^5} (\sin{(x)})= \frac{d}{dx} (\sin{(x)})=\cos{(x)}$

As can be seen above, it can be seen that the continuos derivative of sin (x) is a sequence which repeats after every four terms.

Thus,

$\frac{d^{103}}{dx^{103}} \left(\sin{(x)}\right)= \frac{d^{4(25)+3}}{dx^{4(25)+3}} \left(\sin{(x)}\right) \\ \\ = \frac{d^3}{dx^3} \left(\sin{(x)}\right)=-\cos{(x)}$

Therefore,

$\frac{d^{103}}{dx^{103}} \left(\sin{(x)}\right)=-\cos{(x)}$ .

8 0

3 years ago

If 12x=12−−√11, what value of x makes this equation true?

Solnce55 [7]

Answer:

$\dfrac{1}{11}$

Step-by-step explanation:

Apply exponent rule:

$\sqrt[n]{a} =a^{\frac{1}{n}}$

$\implies \sqrt[11]{12}=12^{\frac{1}{11}}$

$\implies 12^x=12^{\frac{1}{11}}$

$\implies x = \dfrac{1}{11}$

5 0

3 years ago

Read 2 more answers

Jacky baked some biscuits.he kept 3/7 of the biscuits in container A.5/8 of the remainder in container B and rest in container C

Colt1911 [192]

Let "b" represent the number of biscuits Jacky baked.
.. container A holds (3/7)b
.. container B holds (1 -3/7)*(5/8)b = (5/14)b
.. container C holds (1 -3/7 -5/14)b = (3/14)b = 168

Then
.. b = 168/(3/14) = 784

Jacky baked 784 biscuits.

6 0

3 years ago

Please help!! I only have 30 minutes left!! Given that x and y are positive integers and (x·2)+x(2^2)+(y·2^3)+(y·2^4)=42, what i

Viktor [21]

Answer:

xy = 3

Step-by-step explanation:

The expression to be evaluated is:

$2\cdot x +4\cdot x + 8\cdot y + 16\cdot y = 42$