Calculus Examples

$y = e^{x^{2}}$

Step 1

Find the x-intercepts.

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Step 1.1

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

$0 = e^{x^{2}}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $e^{x^{2}} = 0$ .

$e^{x^{2}} = 0$

Step 1.2.2

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{x^{2}}) = \ln (0)$

Step 1.2.3

The equation cannot be solved because $\ln (0)$ is undefined.

Undefined

Step 1.2.4

There is no solution for $e^{x^{2}} = 0$

No solution

Step 1.3

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

x-intercept(s): $None$

Step 2

Find the y-intercepts.

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Step 2.1

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

$y = e^{{(0)}^{2}}$

Step 2.2

Simplify $e^{{(0)}^{2}}$ .

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Step 2.2.1

Raising $0$ to any positive power yields $0$ .

$y = e^{0}$

Step 2.2.2

Anything raised to $0$ is $1$ .

$y = 1$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 1)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 1)$

Step 4