Answer:
a. Maximum= 27, minimum= -5
b. Maximum= 19, minimum=-37
Step-by-step explanation:
We have the function 
. Since the function correspond to a line, then the maximum and minimum values of the function over an interval are in the endpoints of the interval.
Observe that if the line has negative slope then the minimum value is in the right endpoint. If the line has positive slope the minimum value is in the left endpoint of the interval.
The function f(x) has slope m=8. Then
a. the minimum value of f(x) in the interval [0,4] is reach when x=0, and the minimum is 
and the maximum is 
b. the minimum value of f(x) in the interval [-4,,3] is reach when x=-4, and the minimum is 
and the maximum is 
Answer:
-3/2
Step-by-step explanation:
We can find the slope between two points using
m = (y2-y1)/(x2-x1)
= (-7 - -1)/(5 - 1)
(-7+1(/(5-1)
-6/4
-3/2
Answer: 70
Step-by-step explanation:
12*10 = 120-50 = 70
Answer:
The idea is to transform the expression by multiplying 
with its conjugate, 
.
Step-by-step explanation:
For any real number 
and 
, 
.
The factor is irrational. However, when multiplied with its square root conjugate , the product would become rational:
.
The idea is to multiply 
by 
so as to make it easier to take the limit.
Since 
, multiplying the expression by this fraction would not change the value of the original expression.
![\begin{aligned} & \lim\limits_{x \to \infty} \sqrt{x} \, (\sqrt{x + 1} - \sqrt{x}) \\ &= \lim\limits_{x \to \infty} \left[\sqrt{x} \, (\sqrt{x + 1} - \sqrt{x})\cdot \frac{\sqrt{x + 1} + \sqrt{x}}{\sqrt{x + 1} + \sqrt{x}}\right] \\ &= \lim\limits_{x \to \infty} \frac{\sqrt{x}\, ((x + 1) - x)}{\sqrt{x + 1} + \sqrt{x}} \\ &= \lim\limits_{x \to \infty} \frac{\sqrt{x}}{\sqrt{x + 1}+ \sqrt{x}}\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%20%26%20%5Clim%5Climits_%7Bx%20%5Cto%20%5Cinfty%7D%20%5Csqrt%7Bx%7D%20%5C%2C%20%28%5Csqrt%7Bx%20%2B%201%7D%20-%20%5Csqrt%7Bx%7D%29%20%5C%5C%20%26%3D%20%5Clim%5Climits_%7Bx%20%5Cto%20%5Cinfty%7D%20%5Cleft%5B%5Csqrt%7Bx%7D%20%5C%2C%20%28%5Csqrt%7Bx%20%2B%201%7D%20-%20%5Csqrt%7Bx%7D%29%5Ccdot%20%5Cfrac%7B%5Csqrt%7Bx%20%2B%201%7D%20%2B%20%5Csqrt%7Bx%7D%7D%7B%5Csqrt%7Bx%20%2B%201%7D%20%2B%20%5Csqrt%7Bx%7D%7D%5Cright%5D%20%5C%5C%20%26%3D%20%5Clim%5Climits_%7Bx%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%5Csqrt%7Bx%7D%5C%2C%20%28%28x%20%2B%201%29%20-%20x%29%7D%7B%5Csqrt%7Bx%20%2B%201%7D%20%2B%20%5Csqrt%7Bx%7D%7D%20%5C%5C%20%26%3D%20%5Clim%5Climits_%7Bx%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B%5Csqrt%7Bx%7D%7D%7B%5Csqrt%7Bx%20%2B%201%7D%2B%20%5Csqrt%7Bx%7D%7D%5Cend%7Baligned%7D)
.
The order of 
in both the numerator and the denominator are now both 
. Hence, dividing both the numerator and the denominator by 
(same as 
) would ensure that all but the constant terms would approach 
under this limit:
.
By continuity:
.
<span>The base of a triangle exceeds the height by 9 feet. If the area is 180 square feet, find the length of the base and the height of the triangle.</span>
