Answer:
10.2625
Step-by-step explanation:
Just divide by 48
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:
.
Answer:
2(5x + 2)
Step-by-step explanation:
Answer:
6 units
Step-by-step explanation:
We require to calculate the absolute value so as to consider the measure both ways, that is
AB = | 1 - (- 5) | = | 1 + 5 | = 6
BA = | - 5 - 1 | = | - 6 | = 6
Answer:
To convert larger units to smaller units, multiply. When the units are smaller, you need more of them to express the same measure. To convert smaller units to larger units, divide. When the units are larger, you need fewer of them to express the same measure.
Multiply to convert larger units to smaller units.
Divide to convert smaller units to larger units.
When the units are smaller, you need more of them to express the same measure.
When the units are larger, you need fewer of them to express the same measure.
