Answer:
[-3, 3]
Step-by-step explanation:
The range of <em>y = sin x</em> is the interval [-1, 1].
When you multiply the function by -3, you invert the function (symmetry with respect to the x-axis) and stretch is by a factor of 3 vertically.
The range now is [-3, 3]
Answer:
![h'(e) = 7^{e-1}\cdot [7\cdot \ln 7+6\cdot e]](https://tex.z-dn.net/?f=h%27%28e%29%20%3D%207%5E%7Be-1%7D%5Ccdot%20%5B7%5Ccdot%20%5Cln%207%2B6%5Ccdot%20e%5D)
Step-by-step explanation:
Let
, the first derivative of the function is found by applying the concept of implicit differentiation:
(1)
![\ln h(x) = x\cdot \ln f(x)](https://tex.z-dn.net/?f=%5Cln%20h%28x%29%20%3D%20x%5Ccdot%20%5Cln%20f%28x%29)
![\frac{h'(x)}{h(x)}=\ln f(x) +\frac{x\cdot f'(x)}{f(x)}](https://tex.z-dn.net/?f=%5Cfrac%7Bh%27%28x%29%7D%7Bh%28x%29%7D%3D%5Cln%20f%28x%29%20%2B%5Cfrac%7Bx%5Ccdot%20f%27%28x%29%7D%7Bf%28x%29%7D)
![h'(x) = h(x) \cdot \left[\ln f(x)+\frac{x\cdot f'(x)}{f(x)} \right]](https://tex.z-dn.net/?f=h%27%28x%29%20%3D%20h%28x%29%20%5Ccdot%20%5Cleft%5B%5Cln%20f%28x%29%2B%5Cfrac%7Bx%5Ccdot%20f%27%28x%29%7D%7Bf%28x%29%7D%20%5Cright%5D)
![h'(x) = f(x)^{x}\cdot \left[\ln f(x)+\frac{x\cdot f'(x)}{f(x)} \right]](https://tex.z-dn.net/?f=h%27%28x%29%20%3D%20f%28x%29%5E%7Bx%7D%5Ccdot%20%5Cleft%5B%5Cln%20f%28x%29%2B%5Cfrac%7Bx%5Ccdot%20f%27%28x%29%7D%7Bf%28x%29%7D%20%5Cright%5D)
(2)
If we know that
,
and
, then
is:
![h'(e) = 7^{e-1}\cdot [7\cdot \ln 7+6\cdot e]](https://tex.z-dn.net/?f=h%27%28e%29%20%3D%207%5E%7Be-1%7D%5Ccdot%20%5B7%5Ccdot%20%5Cln%207%2B6%5Ccdot%20e%5D)
If 1 equals 20 and 2 equals forty
Then, 3 = 60
4 = 80
5= 100!
Because zero is neither positive nor negative, the term nonnegative is sometimes used to refer to a number that is either positive or zero, while nonpositive is used to refer to a number that is either negative or zero. Zero is a neutral number.
18,267, 2728,2729110,72829183836,261729340