Answer:
Option 1 and 4
Step-by-step explanation:
Answer:
362880 ways
Step-by-step explanation:
The word dragonfly has 9 different letters.
So, to find how many ways this word can be arranged, we just need to calculate the factorial of 9:
First letter has 9 possibilities
Second letter has 8 possibilities (one used)
Third letter has 7 possibilities (two used), and so on.
So the number of ways is:
9*8*7*6*5*4*3*2*1 = 362880 ways
Answer:
Option a.
![\lim_{x \to \frac{\pi}{2}}(3e)^{xcosx}=1](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%283e%29%5E%7Bxcosx%7D%3D1)
Step-by-step explanation:
You have the following limit:
![\lim_{x \to \frac{\pi}{2}{(3e)^{xcosx}](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cfrac%7B%5Cpi%7D%7B2%7D%7B%283e%29%5E%7Bxcosx%7D)
The method of direct substitution consists of substituting the value of
in the function and simplifying the expression obtained.
We then use this method to solve the limit by doing ![x=\frac{\pi}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Cpi%7D%7B2%7D)
Therefore:
![\lim_{x \to \frac{\pi}{2}}{(3e)^{xcosx} = \lim_{x\to \frac{\pi}{2}}{(3e)^{\frac{\pi}{2}cos(\frac{\pi}{2})}](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%7B%283e%29%5E%7Bxcosx%7D%20%3D%20%5Clim_%7Bx%5Cto%20%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%7B%283e%29%5E%7B%5Cfrac%7B%5Cpi%7D%7B2%7Dcos%28%5Cfrac%7B%5Cpi%7D%7B2%7D%29%7D)
![cos(\frac{\pi}{2})=0\\](https://tex.z-dn.net/?f=cos%28%5Cfrac%7B%5Cpi%7D%7B2%7D%29%3D0%5C%5C)
By definition, any number raised to exponent 0 is equal to 1
So
![\lim_{x\to \frac{\pi}{2}}{(3e)^{\frac{\pi}{2}cos(\frac{\pi}{2})} = \lim_{x\to \frac{\pi}{2}}{(3e)^{\frac{\pi}{2}(0)}\\\\](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto%20%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%7B%283e%29%5E%7B%5Cfrac%7B%5Cpi%7D%7B2%7Dcos%28%5Cfrac%7B%5Cpi%7D%7B2%7D%29%7D%20%3D%20%5Clim_%7Bx%5Cto%20%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%7B%283e%29%5E%7B%5Cfrac%7B%5Cpi%7D%7B2%7D%280%29%7D%5C%5C%5C%5C)
![\lim_{x\to \frac{\pi}{2}}{(3e)^{0}} = 1](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto%20%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%7B%283e%29%5E%7B0%7D%7D%20%3D%201)
Finally
![\lim_{x \to \frac{\pi}{2}}(3e)^{xcosx}=1](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%283e%29%5E%7Bxcosx%7D%3D1)
Answer:
63
Step-by-step explanation:
(6+9÷3)×7
division is always first
(6+3)×7
then parenthesis
9×7
multiply
63
7 1/3
I think this is it, i would like for u to get a second opinion.