MaxWong

1(a) $500 x (1+2%)^{25 x 12}

    = $500 x 1.02³⁰

     = $905.6807920516769 

    $\approx$ $ 905.68

(b)(i)$\quad(\frac{1+0.0339}{1})^1-1\\ = 0.0339$

APR = 3.39%

(b)(ii) $\quad (\frac{2+0.0329}{2})^2-1\\ = 0.033170602.....$

APR = 3.32.....%

(b)(iii) $\quad (\frac{4+0.0335}{4})^4-1\\ = 0.033923......$

APR = 3.392.....%

(b)(iv) $\quad (\frac{12+0.034}{12})^{12}-1\\=0.0345348......$

APR = 3.45......%

Which of these gives the cheapest option when taking out a loan for two years?

3.29% p.a. compounded semi-annually.

How much interest would it cost to borrow $1,000 for two years under the cheapest option?

1000 x 3.32% x 2

= $66.4

(c) 1000 x (1+2.5%)^{4 x 10}

= 1000 x 2.685063838

= $2685.1 approx.

(d) f(x) = 2 - 3ln(x) + 3x

$f'(x)= \frac{3}{x}+3\\ f'(1)= \frac{3}{1}+3 = 6$

f(x) = 2x²e^x

$f'(x)= 2xe^x(x+2)\\ f'(1)= 2(1)(e)(1+2)= 6e$

g(x) = 1 + x²

$g'(x)= 2x\\ g'(1)= 2(1)=2$

(e) $f(x)=x^3-2x^2-4x\\ f'(x)= 3x^2-4x-4\\ f''(x)= 6x-4$

I don't know what's critical point and local maximum.......

Why can't I edit my answer again..... Never mind.

If you want to type a degree sign do {something}^{\circ}

Example: $180^{\circ}$ Latex code: 180^{\circ}

$Interior \space angle \space sum \space of \space a\space 9\space sided \space polygon\\={(9-2)\times180^{\circ}}\\=1260^{\circ}$

It is a kind of machine that follows the 'IPO'.

Input : You input an equation in the calc.

Process: The calc. help you calculate.

Output: The result is the output of the calc.

And this could be done within a second.

Then join the forum! :D 

E.g.

1) $\frac{7}{21}=\frac{7\div7}{21\div7}=\frac{1}{3}$

2)$\frac{108}{216}=\frac{108\div108}{216\div108}=\frac{1}{2}$

3)$\frac{45}{150}=\frac{45\div15}{150\div15}=\frac{3}{10}$

$-\frac{2}{3}\times \frac{1}{3}=-\frac{2}{9}$

LaTeX code: -\frac{2}{3}\times \frac{1}{3} = -\frac{2}{9}

$y=\frac{1}{2}x+1\\ y= -3x+8$_------(2)^------(1)

(1)-(2): 0 = $\frac{7}{2}x-7$

        $\frac{7}{2}x=7\\x=2$

$y = (\frac{1}{2})(2)+1\\y=1+1\\y=2$

If it's a maths question, it's 19

If it's a joke, it's 21

and I don't know why 9+10=21 is a joke.

log(number) <-- For logarithms of base 10.

ln(number)<-- For logarithms of base e.

log(number1 , number2) <-- For logarithms of base (number2)