Calculus Examples

$x - \ln (x)$

Step 1

Write $x - \ln (x)$ as an equation.

$y = x - \ln (x)$

Step 2

Find the x-intercepts.

Tap for more steps...

Step 2.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = x - \ln (x)$

Step 2.2

Solve the equation.

Tap for more steps...

Step 2.2.1

Remove parentheses.

$0 = x - \ln (x)$

Step 2.2.2

Graph each side of the equation. The solution is the x-value of the point of intersection.

No solution

Step 2.3

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

x-intercept(s): $None$

Step 3

Find the y-intercepts.

Tap for more steps...

Step 3.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = (0) - \ln (0)$

Step 3.2

Solve the equation.

Tap for more steps...

Step 3.2.1

The natural logarithm of zero is undefined.

$y = Undefined$

Step 3.2.2

Remove parentheses.

$y = (0) - \ln (0)$

Step 3.2.3

The equation cannot be solved because it is undefined.

$Undefined$

Step 3.3

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

y-intercept(s): $None$

Step 4

List the intersections.

x-intercept(s): $None$

y-intercept(s): $None$

Step 5