Calculus 2 : Finding Limits and One-Sided Limits
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Example Question #324 : Limits
Evaluate the following limit:
To evaluate the limit as x approaches infinity, we must factor out a term consisting of the highest power term divided by itself (so we are unchanging the limit):
The first term cancels to become 1, and the negative exponent terms go to zero when x approaches infinity (infinity in the denominator makes zero), so what we are left with is
Example Question #325 : Limits
Evaluate the limit:
The limiting situation in this equation would be the denominator. Plug the value that x is approaching into the denominator to see if the denominator will equal 0. In this question, the denominator will not equal zero when x=1; so we proceed to insert the value of x into the entire equation.
Example Question #326 : Limits
Evaluate the limit:
The limiting situation in this equation would be the denominator. Plug the value that x is approaching into the denominator to see if the denominator will equal 0. In this question, the denominator will not equal zero when x=2; so we proceed to insert the value of x into the entire equation.
Example Question #327 : Limits
Evaluate the limit:
We see that we cannot factor this to make the denominator not equal 0; hence this limit DNE because the denominator is zero.
Example Question #328 : Limits
Evaluate the limit:
The limiting situation in this equation would be the denominator. Plug the value that x is approaching into the denominator to see if the denominator will equal 0. In this question, the denominator will not equal zero when x=5; so we proceed to insert the value of x into the entire equation.
Example Question #329 : Limits
Evaluate the limit:
The limiting situation in this equation would be the denominator. Plug the value that x is approaching into the denominator to see if the denominator will equal 0. In this question, the denominator will not equal zero when x=6; so we proceed to insert the value of x into the entire equation.
Example Question #330 : Limits
Evaluate the limit:
The limiting situation in this equation would be the denominator. Plug the value that x is approaching into the denominator to see if the denominator will equal 0. In this question, the denominator will not equal zero when x=7; so we proceed to insert the value of x into the entire equation.
Example Question #331 : Limits
Evaluate the limit:
There is no limiting situation in this equation (like a denominator) so we can just plug in the value that n approaches into the limit and solve:
Example Question #332 : Limits
Evaluate the limit:
There is no limiting situation in this equation (like a denominator) so we can just plug in the value that n approaches into the limit and solve:
Example Question #333 : Limits
Evaluate the limit:
The limiting situation in this equation would be the denominator. Plug the value that x is approaching into the denominator to see if the denominator will equal 0. In this question, the denominator will not equal zero when x=10; so we proceed to insert the value of x into the entire equation.
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