The limit of $x$ minus sine of angle $x$ divided by $x$ cube should be evaluated in this limit problem as the value of $x$ approaches zero. Firstly, let us try to evaluate the limit by direct substitution. Now, substitute $x$ is equal to zero in the rational function.
The sine of zero radian is equal to zero as per the trigonometric mathematics.
It is evaluated as per the direct substitution method that the limit of variable $x$ minus sine of angle $x$ divided by cube of $x$ is indeterminate as the value of $x$ tends to zero. It clears to us that the direct substitution method is not useful to find the limit initially.
Learn how to calculate the limit of $x$ minus sine of angle $x$ divided by the cube of $x$ as $x$ tends to zero by using change of variables.
Learn how to use the l’hôpital’s rule to find the limit of $x$ minus sine of angle $x$ divided by $x$ cube as $x$ approaches zero.
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