Calculus Examples

$lim_{x \to 0} (x^{2}) \csc^{2} (1) x$

Step 1

Move the term $\csc^{2} (1)$ outside of the limit because it is constant with respect to $x$ .

$\csc^{2} (1) lim_{x \to 0} x^{2} x$

Step 2

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $0$ .

$\csc^{2} (1) lim_{x \to 0} x^{2} \cdot lim_{x \to 0} x$

Step 3

Move the exponent $2$ from $x^{2}$ outside the limit using the Limits Power Rule.

$\csc^{2} (1) {(lim_{x \to 0} x)}^{2} \cdot lim_{x \to 0} x$

Step 4

Evaluate the limits by plugging in $0$ for all occurrences of $x$ .

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Step 4.1

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$\csc^{2} (1) \cdot 0^{2} \cdot lim_{x \to 0} x$

Step 4.2

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$\csc^{2} (1) \cdot 0^{2} \cdot 0$

Step 5

Simplify the answer.

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Step 5.1

Multiply $0^{2}$ by $0$ by adding the exponents.

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Step 5.1.1

Move $0$ .

$\csc^{2} (1) \cdot (0 \cdot 0^{2})$

Step 5.1.2

Multiply $0$ by $0^{2}$ .

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Step 5.1.2.1

Raise $0$ to the power of $1$ .

$\csc^{2} (1) \cdot (0^{1} \cdot 0^{2})$

Step 5.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\csc^{2} (1) \cdot 0^{1 + 2}$

Step 5.1.3

Add $1$ and $2$ .

$\csc^{2} (1) \cdot 0^{3}$

Step 5.2

Evaluate $\csc (1)$ .

${57.29868849}^{2} \cdot 0^{3}$

Step 5.3

Raise $57.29868849$ to the power of $2$ .

$3283.13970365 \cdot 0^{3}$

Step 5.4

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

$3283.13970365 \cdot 0$

Step 5.5

Multiply $3283.13970365$ by $0$ .

$0$