Question

The area of the triangle formed by the coordinate axes and tangent to the curve $y={\log }_{e}x$ at $(1,0)$ is

• A. $1$
• B. $\frac{1}{2}$
• C. $2$
• D. $\frac{3}{2}$

Answer 1

The correct option is B $\frac{1}{2}$

Given,
$y={\log }_{e}x\Rightarrow y^{\prime }=\frac{1}{x}$
Putting $(1,0)$
$y^{\prime }=1$
Equation of the tangent:
$\frac{y-0}{x-1}=1\Rightarrow y=x-1$


Hence, the area of the triangle formed by the coordinate axis and tangent to the curve $y={\log }_{e}x$ at $(1,0)$ is
$\frac{1}{2}\times 1\times 1=\frac{1}{2}$ sq. units