Question

The point P(5, −4) lies on the curve y = 4/(4 − x).

Answer 1

Answer:

4

Step-by-step explanation:

Slope refers to the steepness of the line.

Slope is equal to change in value of y divided by change in value of x.

The slope of the secant line is given by $\frac{f(x)-f(a)}{x-a}$.

Given points are $P\left ( 5,-4 \right )\,,\,Q\left ( x,\frac{4}{4-x} \right )$

So, slope of the secant line is $\frac{\frac{4}{4-x}+4}{x-5}=\frac{4+4(4-x)}{(x-5)(4-x)}=\frac{20-4x}{(x-5)(4-x)}=\frac{-4(x-5)}{(x-5)(4-x)}=\frac{-4}{4-x}=\frac{4}{x-4}$

(i) At x = 4.9,

$\frac{4}{4.9-4}=\frac{4}{0.9}=4.444444$

(ii) At x = 4.99,

$\frac{4}{4.99-4}=\frac{4}{0.99}=4.040404$

(iii) At x = 4.999,

$\frac{4}{4.999-4}=\frac{4}{0.999}=4.004004$

(iv) At x = 4.9999,

$\frac{4}{4.9999-4}=\frac{4}{0.9999}=4.0004$

(v) At x =5.1,

$\frac{4}{5.1-4}=\frac{4}{1.1}=3.636364$

(vi)

At x = 5.01,

$\frac{4}{5.01-4}=\frac{4}{1.01}=3.960396$

(vii) At x = 5.001,

$\frac{4}{5.001-4}=\frac{4}{1.001}=3.996004$

(viii) At x = 5.0001,

$\frac{4}{5.0001-4}=\frac{4}{1.0001}=3.9996$

(b)

Slope of the tangent line is 4.