Don't forget to follow me!!!
We can find this using the formula: L= ∫√1+ (y')² dx
First we want to solve for y by taking the 1/2 power of both sides:
y=(4(x+1)³)^1/2
y=2(x+1)^3/2
Now, we can take the derivative using the chain rule:
y'=3(x+1)^1/2
We can then square this, so it can be plugged directly into the formula:
(y')²=(3√x+1)²
<span>(y')²=9(x+1)
</span>(y')²=9x+9
We can then plug this into the formula:
L= ∫√1+9x+9 dx *I can't type in the bounds directly on the integral, but the upper bound is 1 and the lower bound is 0
L= ∫(9x+10)^1/2 dx *use u-substitution to solve
L= ∫u^1/2 (du/9)
L= 1/9 ∫u^1/2 du
L= 1/9[(2/3)u^3/2]
L= 2/27 [(9x+10)^3/2] *upper bound is 1 and lower bound is 0
L= 2/27 [19^3/2-10^3/2]
L= 2/27 [√6859 - √1000]
L=3.792318765
The length of the curve is 2/27 [√6859 - √1000] or <span>3.792318765 </span>units.
Answer:
The final balance is £1,720.
The total compound interest is £520
you don't even to round it at all
The equation of the horizontal asymptote for this function f(x) = (1/2)^x + 3 is option D y = 3.
<h3>When do we get horizontal asymptote for a function?</h3>
The line y = a is horizontal asymptote if the function f(x) tends to 'a' from the upside of that line y = a, or from downside of that line.
The function is given as;
f(x) = (1/2)^x + 3
The function is Exponential functions.
Exponential functions have a horizontal asymptote.
The equation of the horizontal asymptote is option D y = 3.
Learn more about horizontal asymptotes here:
brainly.com/question/2513623
#SPJ1
