PLSSSS HELPP ASSPPPP!!!!
1 answer:
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Answer:
See Below.
Step-by-step explanation:
Problem 1)
We want to verify that:
Note that cot(x) = cos(x) / sin(x). Hence:
Multiply:
Recall that Pythagorean Identity: sin²(x) + cos²(x) = 1 or cos²(x) = 1 - sin²(x). Substitute:
Split:
Simplify:
Problem 2)
We want to verify that:
Square:
Convert csc(x) to 1 / sin(x) and cot(x) to cos(x) / sin(x). Thus:
Factor out the sin²(x) from the denominator:
Factor (perfect square trinomial):
Using the Pythagorean Identity, we know that sin²(x) = 1 - cos²(x). Hence:
Factor (difference of two squares):
Factor out a negative from the first factor in the denominator:
Cancel:
Distribute the negative into the numerator. Therefore:
For the function to be differentiable, its derivative has to exist everywhere, which means the derivative itself must be continuous. Differentiating gives
The question mark is a placeholder, and if the derivative is to be continuous, then the question mark will have the same value as the limit as
from either side.
So the derivative will be continuous as long as
For the function to be differentiable everywhere, we need to require that
is itself continuous, which means the following limits should be the same:
So, the function should be
with derivative
The question mark is a placeholder, and if the derivative is to be continuous, then the question mark will have the same value as the limit as
So the derivative will be continuous as long as
For the function to be differentiable everywhere, we need to require that
So, the function should be
with derivative
Answer:
a)
b) 86.5 years
Step-by-step explanation:
All values are rounded to 2 decimal places
a) We can find line by using y =mx+b
Therefore the line of best fit is
b) We can do this by using the formula of the best fit line to estimate the life expectancy of someone born in 2005
Therefore the estimated life expectancy of someone born in 2005 is 86.5 years
PS. Please give brainliest answer this was a lot of working out