you make sure it’s done before the detailing process ! this is so you can begin the process without ruining the original piece.
if you were to pull straight up, it would damage the area around it by cracking or removing ♡
xtan-1x differentiate using first principle
Answer:
[tex]F'(x) = \frac{x}{{1 +x^{2} } } + tan^{-1} (x)}[/tex]
Explanation:
Given - F(x) = xtan⁻¹x
To find - Differentiate using first principle
Formula used -
First Principal :
F'(x) = [tex]\lim_{h \to 0} \frac{f(x+h) - f(x)}{h}[/tex]
and
[tex]tan^{-1}(A - B) = tan^{-1}(\frac{A - B}{1 + AB} )[/tex]
Proof -
Given that, F(x) = xtan⁻¹x
⇒F(x+h) = (x+h) tan⁻¹(x+h)
So,
[tex]F'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}\\= \lim_{h \to 0} \frac{(x+h)tan^{-1} (x+h) - xtan^{-1} x}{h}\\= \lim_{h \to 0} \frac{xtan^{-1} (x+h) + htan^{-1} (x+h) - xtan^{-1} x}{h}\\= \lim_{h \to 0} \frac{x(tan^{-1} (x+h) - tan^{-1} x) + htan^{-1} (x+h)}{h}\\= \lim_{h \to 0} \frac{x}{h} (tan^{-1} (x+h) - tan^{-1} x) + tan^{-1} (x+h)}[/tex]
Now,
We know that,
[tex]tan^{-1}(A - B) = tan^{-1}(\frac{A - B}{1 + AB} )[/tex]
[tex]F'(x) = \lim_{h \to 0} \frac{x}{h} (tan^{-1} (x+h) - tan^{-1} x) + tan^{-1} (x+h)}\\= \lim_{h \to 0} \frac{x}{h} tan^{-1} (\frac{(x+h) - x}{1 + (x+h)x}) + tan^{-1} (x+h)}\\= \lim_{h \to 0} \frac{x}{h} tan^{-1} (\frac{h}{1 + (x+h)x}) + tan^{-1} (x+h)}\\\\= \lim_{h \to 0} \frac{x}{h\frac{1 + x(x+h)}{1 +x(x+h)} } tan^{-1} (\frac{h}{1 + (x+h)x}) + tan^{-1} (x+h)}\\= \lim_{h \to 0} \frac{x}{{1 +x(x+h)} }.\frac{1 +x(x+h)}{h} tan^{-1} (\frac{h}{1 + (x+h)x}) + tan^{-1} (x+h)}[/tex]
Now,
We know that,
[tex]\lim_{h \to 0} \frac{tan^{-1} x}{x} = 1[/tex]
∴ we get
[tex]F'(x) = \lim_{h \to 0} \frac{x}{{1 +x(x+h)} }.\frac{1 +x(x+h)}{h} tan^{-1} (\frac{h}{1 + (x+h)x}) + tan^{-1} (x+h)}\\ = \lim_{h \to 0} \frac{x}{{1 +x(x+h)} }.\lim_{h \to 0}\frac{1 +x(x+h)}{h} tan^{-1} (\frac{h}{1 + (x+h)x}) + \lim_{h \to 0}tan^{-1} (x+h)}\\= \frac{x}{{1 +x(x+0)} }.1 + tan^{-1} (x+0)}\\= \frac{x}{{1 +x(x)} } + tan^{-1} (x)}\\= \frac{x}{{1 +x^{2} } } + tan^{-1} (x)}[/tex]
So,
We get
[tex]F'(x) = \frac{x}{{1 +x^{2} } } + tan^{-1} (x)}[/tex]
Which of the following is typical of the selection of survey participants? They can indicate partiality toward a group. They must be surveyed more than once. They can be selected on purpose by a researcher. They must be representative of the population.
Answer:
Option D
Explanation:
In general a sample collected from a set of naturally distributed data set must also follow the bell curve or natural distribution
In other way round it can be said that sample set must have the same characteristics as that of the main set and hence a sample must be representative of the population.
Option D is correct
Answer:
the answer is they must be representative of the population.
Explanation:
I took the test and got it right.
What is the approximate time of death if the body temperature was 50°F?
The approximate time of death of a body whose temperature was 50°F = 48.6 hours
How to calculate time of death?The time of death is your by the forensic experts for investigation purposes.
The body loses 1 °F every one hour.
The human body is = 98.6*F
Therefore, to calculate the time of death of the body whose temperature is 50°F = 98.6 - 50
= 48.6 × 1 hour = 48.6 hours
Learn more about forensic science here:
https://brainly.com/question/19238665