Question

Find the slope of the curve y=2/x at x=a.​

Answer 1

Answer:

• We are given:- y=2/x
• We need to find the slope of the curve at x=a.

Step-by-step explanation:

Solution,

We use the slope formula, setting x=a :

$\displaystyle{{{{ \lim_{h \to0}}}} \frac{ \frac{2}{x + h} - \frac{2}{x} }{h} = \lim_{h \to0} \frac{ \frac{2}{a + h} - \frac{2}{a} }{h} }$

$\displaystyle{ \lim_{h \to0} \frac{ \frac{2a - 2(a + h)}{a(a + h)} }{h} = \displaystyle{ \lim_{h \to0} \frac{2a - 2(a + h)}{ha(a + h)} }}$

$\displaystyle{ \lim_{h \to0} \frac{2a - 2a - 2h}{ha(a + h)} = \displaystyle{ \lim_{h \to0} \frac{ - 2h}{ha(a + h)} }}$

$\displaystyle{ \lim_{h \to0} \frac{ - 2}{a(a + h)} = - \frac{ 2}{ {a}^{2} } }$

Therefore, The slope of the curve y=2/x at x=a is -2/a^2.