12000 > 3000+25x Or you can write it out as (12000-3000)/25=x
Simplifying h(x) gives
h(x) = (x² - 3x - 4) / (x + 2)
h(x) = ((x² + 4x + 4) - 4x - 4 - 3x - 4) / (x + 2)
h(x) = ((x + 2)² - 7x - 8) / (x + 2)
h(x) = ((x + 2)² - 7 (x + 2) - 14 - 8) / (x + 2)
h(x) = ((x + 2)² - 7 (x + 2) - 22) / (x + 2)
h(x) = (x + 2) - 7 - 22/(x + 2)
h(x) = x - 5 - 22/(x + 2)
An oblique asymptote of h(x) is a linear function p(x) = ax + b such that

In the simplified form of h(x), taking the limit as x gets arbitrarily large, we obviously have -22/(x + 2) converging to 0, while x - 5 approaches either +∞ or -∞. If we let p(x) = x - 5, however, we do have h(x) - p(x) approaching 0. So the oblique asymptote is the line y = x - 5.
Answer:
(a) k'(0) = f'(0)g(0) + f(0)g'(0)
(b) m'(5) = 
Step-by-step explanation:
(a) Since k(x) is a function of two functions f(x) and g(x) [ k(x)=f(x)g(x) ], so for differentiating k(x) we need to use <u>product rule</u>,i.e., ![\frac{\mathrm{d} [f(x)\times g(x)]}{\mathrm{d} x}=\frac{\mathrm{d} f(x)}{\mathrm{d} x}\times g(x) + f(x)\times\frac{\mathrm{d} g(x)}{\mathrm{d} x}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20%5Bf%28x%29%5Ctimes%20g%28x%29%5D%7D%7B%5Cmathrm%7Bd%7D%20x%7D%3D%5Cfrac%7B%5Cmathrm%7Bd%7D%20f%28x%29%7D%7B%5Cmathrm%7Bd%7D%20x%7D%5Ctimes%20g%28x%29%20%2B%20f%28x%29%5Ctimes%5Cfrac%7B%5Cmathrm%7Bd%7D%20g%28x%29%7D%7B%5Cmathrm%7Bd%7D%20x%7D)
this will give <em>k'(x)=f'(x)g(x) + f(x)g'(x)</em>
on substituting the value x=0, we will get the value of k'(0)
{for expressing the value in terms of numbers first we need to know the value of f(0), g(0), f'(0) and g'(0) in terms of numbers}{If f(0)=0 and g(0)=0, and f'(0) and g'(0) exists then k'(0)=0}
(b) m(x) is a function of two functions f(x) and g(x) [
]. Since m(x) has a function g(x) in the denominator so we need to use <u>division rule</u> to differentiate m(x). Division rule is as follows : 
this will give <em>
</em>
on substituting the value x=5, we will get the value of m'(5).
{for expressing the value in terms of numbers first we need to know the value of f(5), g(5), f'(5) and g'(5) in terms of numbers}
{NOTE : in m(x), g(x) ≠ 0 for all x in domain to make m(x) defined and even m'(x) }
{ NOTE :
}
Answer:
3
Step-by-step explanation:
- <em>Each of the seven happy clowns has a red nose.</em>
This means there are (15-7) 8 sad clowns.
- <em>Five of the sad clowns have red noses. </em>
This means out of 8 sad clowns, 5 have red noses. So the clowns that have to act sad and have red noses are (8-5) 3.
This is not an appropriate way of completing your homework.