Calculus Examples

$y = \frac{e^{x}}{x}$ , $(1, e)$

Step 1

Find the value of $m$ using the formula for the equation of a line.

$y = m x + b$

Step 2

Substitute the value of $b$ into the equation.

$y = m x + \frac{e^{x}}{x}$

Step 3

Substitute the value of $x$ into the equation.

$y = m (1) + \frac{e^{1}}{1}$

Step 4

Substitute the value of $y$ into the equation.

$e = m (1) + \frac{e^{1}}{1}$

Step 5

Find the value of $m$ .

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Step 5.1

Rewrite the equation as $m (1) + \frac{e}{1} = e$ .

$m (1) + \frac{e}{1} = e$

Step 5.2

Simplify each term.

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Step 5.2.1

Multiply $m$ by $1$ .

$m + \frac{e}{1} = e$

Step 5.2.2

Divide $e$ by $1$ .

$m + e = e$

Step 5.3

Move all terms not containing $m$ to the right side of the equation.

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Step 5.3.1

Subtract $e$ from both sides of the equation.

$m = e - e$

Step 5.3.2

Subtract $e$ from $e$ .

$m = 0$

Step 6

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = \frac{e^{x}}{x}$

Step 7