# Cambridge Prelim MX1 Textbook Marathon/Q&A (1 Viewer)

#### a_t

##### New Member
Need help with this please. Q2A of Ex 7B
For each function below, simplify f(x + h) − f(x) / h , then take lim h→0 to find the derivative.

(a) f(x) = 5x + 1

#### 1729

##### Active Member
Need help with this please. Q2A of Ex 7B
For each function below, simplify f(x + h) − f(x) / h , then take lim h→0 to find the derivative.

(a) f(x) = 5x + 1
\noindent \begin{align*}\frac{f(x+h) - f(x)}{h} &= \frac{[5(x+h) + 1] - (5x+1)}{h} \\ &= \frac{5x + 5h + 1 - 5x - 1}{h} \\ &= \frac{5h}{h} \\ &= 5 \end{align*} \\ And so f'(x) = \lim_{h \rightarrow 0}\frac{f(x+h) - f(x)}{h} = \lim_{h \rightarrow 0}5 = 5 \\ ie. f'(x) = 5.

#### joelle_kk

##### New Member
Need Help!!! 2H 16a & b
Three tourists T1, T2 and T3 at ground level are observing a landmark L. T1 is due north of L, T3 is due east of L, and T2 is on the line of sight from T1 and T3 and between them. The angles of elevation to the top of L from T1, T2 and T3 are 25', 32' and 36' respectively.

a) show tan angle LT1T2 = cot 36 / cot 25
b) use the sine rule in triangle LT1T2 to find, correct to the nearest minute, the bearing of T2 from L

#### Pakka

##### New Member

Pls provide full working. Thanks

#### Drongoski

##### Well-Known Member
View attachment 34573
Pls provide full working. Thanks
Use change of base formula:

$log _{ab} x = \frac {log _a x}{log _a (ab)} = \frac {log _a x}{log _a a + log _a b} = \frac {log _a x}{1 + log _a b}$

#### gilgamesh1121

##### New Member

I'd appreciate working for 19b. thanks

#### fan96

##### 617 pages
$\frac{1+\sqrt{1+\frac{\sqrt{3}}2}}{\sqrt{1+\frac{\sqrt{3}}2}} \cdot \frac 22$

$= \frac{2+\sqrt{4+2\sqrt3}}{\sqrt{4+2\sqrt3}}$

$= \frac{3 + \sqrt3}{\sqrt 3 + 1}$

$= \frac{\sqrt 3 (\sqrt3+1)}{\sqrt 3 + 1}$

$= {\sqrt 3}$