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 : 
}
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Answer:
Explained below.
Step-by-step explanation:
The regression equation to predict amount of precipitation (in inches) in July from the average high temperatures (in degrees Fahrenheit) in July is as follows:
PRECIP = 2.0481 + 0.0067 HIGH
(1)
The value of the slope of the regression line is, 0.0067.
(2)
The predictor variable in this context is the average high temperatures (in degrees Fahrenheit) in July.
(3)
The response variable in this context is the amount of precipitation (in inches) in July.
(4)
The slope of a regression line is average rate of change in the dependent variable with one unit change in the independent variable.
The slope here is 0.0067.
This value implies that the average rate of change in the amount of precipitation (in inches) in July increases by 0.0067 inches with every 1°F increase in the average high temperatures.
(5)
Compute the mount of precipitation for a city that has an average high temperature in July of 87.31°F as follows:
PRECIP = 2.0481 + 0.0067 HIGH
= 2.0481 + 0.0067 × 87.31°F
= 2.633077
≈ 2.63 inches.
The value of b is -6.
Explanation:
The expression is 
To determine the value of b, we shall solve the expression.
Applying exponent rule, 
, we get,
Applying exponent rule, 
, we have,
The expression is of the form, 
then 
Applying this rule, we get,
Dividing both sides by 4, we have,
Hence, the value of b is -6.
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