Recall the Pythagorean identity,
![1-\cos^2t=\sin^2t](https://tex.z-dn.net/?f=1-%5Ccos%5E2t%3D%5Csin%5E2t)
To get this expression in the fraction, multiply the numerator and denominator by
:
![\dfrac{t\sin t}{1-\cos t}\cdot\dfrac{1+\cos t}{1+\cos t}=\dfrac{t\sin t(1+\cos t)}{\sin^2t}=\dfrac{t(1+\cos t)}{\sin t}](https://tex.z-dn.net/?f=%5Cdfrac%7Bt%5Csin%20t%7D%7B1-%5Ccos%20t%7D%5Ccdot%5Cdfrac%7B1%2B%5Ccos%20t%7D%7B1%2B%5Ccos%20t%7D%3D%5Cdfrac%7Bt%5Csin%20t%281%2B%5Ccos%20t%29%7D%7B%5Csin%5E2t%7D%3D%5Cdfrac%7Bt%281%2B%5Ccos%20t%29%7D%7B%5Csin%20t%7D)
Now,
![\displaystyle\lim_{t\to0}\frac{t\sin t}{1-\cos t}=\lim_{t\to0}\frac t{\sin t}\cdot\lim_{t\to0}(1+\cos t)](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bt%5Cto0%7D%5Cfrac%7Bt%5Csin%20t%7D%7B1-%5Ccos%20t%7D%3D%5Clim_%7Bt%5Cto0%7D%5Cfrac%20t%7B%5Csin%20t%7D%5Ccdot%5Clim_%7Bt%5Cto0%7D%281%2B%5Ccos%20t%29)
The first limit is well-known and equal to 1, leaving us with
![\displaystyle\lim_{t\to0}(1+\cos t)=1+\cos0=\boxed{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bt%5Cto0%7D%281%2B%5Ccos%20t%29%3D1%2B%5Ccos0%3D%5Cboxed%7B2%7D)
Answer:
A)t=9w+25. T=12w+10
Step-by-step explanation:
Equation for you:
t = 25 + 9w
Equation for friend:
t = 10 + 12w
The answer to this problem is 1 5/12
Value of x is 21
Step-by-step explanation:
- Step 1: Find x given that ∠NLW = 90° and is equal to 1/3(12x + 18)
⇒ 90 = 1/3(12x + 18)
⇒ 270 = 12x + 18
⇒ 252 = 12x
∴ x = 252/12 = 21
Im not sure wym but i think the answer is 20