Answer:
2π or 0π are the only points that satisfy the expression, but since the restriction is 0 <= x < 2π
the answer would be 0π
For what values of b will F(x) = logb x be an increasing function?
2 answers:
In order to answer you need to keep in mind what is a logarithm:
logb x = n is the equivalent of asking "you should raise the base b <span>to <span>what number n</span></span> in order to get x?": bⁿ = x
From this follows that b must be positive, otherwise the function is not defined everywhere in R: for example, take log(-2) x = 0.5 ? This means:
=√(-2) which is impossible in R.
Therefore, both answers A and C are not correct because they take in consideration negative values.
If we take the base between 0 and 1 excluded, we have a fraction whose denominator is bigger than the numerator. Such a fraction, elevated to increasing exponents get smaller, for example:
(1/2)² = 1/4
(1/2)³ = 1/8
(1/2)⁴ = 1/16
Therefore the function is dereasing and answer B is incorrect.
The right answer is, therefore, D) b > 1.
logb x = n is the equivalent of asking "you should raise the base b <span>to <span>what number n</span></span> in order to get x?": bⁿ = x
From this follows that b must be positive, otherwise the function is not defined everywhere in R: for example, take log(-2) x = 0.5 ? This means:
Therefore, both answers A and C are not correct because they take in consideration negative values.
If we take the base between 0 and 1 excluded, we have a fraction whose denominator is bigger than the numerator. Such a fraction, elevated to increasing exponents get smaller, for example:
(1/2)² = 1/4
(1/2)³ = 1/8
(1/2)⁴ = 1/16
Therefore the function is dereasing and answer B is incorrect.
The right answer is, therefore, D) b > 1.
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Answer:
Area of Trapezoid is 39 unit²
Step-by-step explanation:
Given as :
For A Trapezoid
The measure of base side 1 = = 10 unit
The measure of base side 2 = = 16 unit
The height of the Trapezoid = h = 3 unit
Let The Area of Trapezoid = A square unit
<u>Now, From Formula</u>
Area of Trapezoid = × (sum of opposite base) × height
I.e A = × (
+
) × h
Or, A = × (10 unit + 16 unit) × 3 unit
Or, A = × (26 unit) × 3 unit
Or, A = × 78 unit²
Or, A = unit²
I.e A = 39 unit²
So, The Area of Trapezoid = A = 39 unit²
Hence, The Area of Trapezoid is 39 unit² . Answer