You've established that
so all you need to do is compute the integral. Rewrite the integrand as
and replace
, so that
. Then
By the fundamental theorem of calculus, this evaluates to
and so the series converges.
You also could have used the fact that the series is geometric with common ratio less than 1 to arrive at the same conclusion, with the added perk of being able to find the exact value of the sum to corroborate this.
Answer:
True
Step-by-step explanation:
true ∧ (not false) . . . . . . . has a truth value of <em>True</em>
_____
The "and" operator gives <em>true</em> if all of its operands are <em>true</em>.
We try to represent each number inside the square root as a product of a square and another number.
a) 7√32 - 5√2 + √8
√32 = √(16 *2) = √16 * √2 = 4* √2 = 4√2
√8 = √(4 *2) = √4 * √2 = 2* √2 = 2√2
7√32 - 5√2 + √8 = 7*(4√2) - 5√2 + 2√2 =
= 28√2 - 5√2 + 2√2 Factorize out √2
= (28 - 5 + 2)√2
= 25√2
b) 2√150 - 4√54 + 6√24
√150 = √(25 * 6) = √25 * √6 = 5*√6 = 5√6
√54 = √(9 * 6) = √9 * √6 = 3*√6 = 3√6
√24 = √(4 * 6) = √4 * √6 = 2*√6 = 2√6
2√150 - 4√54 + 6√24 = 2*(5√6) - 4*(3√6) + 6*(2√6)
= 2*5√6 - 4*3√6 + 6*2√6
= 10√6 - 12√6 + 12√6 Factorize √6
= (10 - 12 + 12)√6
= 10√6
Answer:
no
Step-by-step explanation:
they can be either side because the numbers are different in the angles
Answer:
1,946,075.95 AED
Step-by-step explanation:
Firstly, we write the general formula for an exponential increase as follows;
V(t) = A( 1 + r)^t
where V(t) is the value after some number of years t
A is the investment amount which is 100,000 AED
r is the rate of increase which is 16% = 16/100 = 0.16
t is the number of years which is 20
substituting these values;
V(20) = 100,000( 1 + 0.16)^20
V(20) = 100,000(1.16)^20
V(20) = 1,946,075.95 AED
