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Evaluating limits using change of variable/ variable substitution

Hi there! I am currently in grade 12, studying calculus 30 which is just calculus. I have a question about the above topic posted. One contains roots and I'm not sure exactly how to solve it. Any help would be great!

1) lim ( X^1/3 - 3) / (x - 27)

X-->27

2) lim. (square root of x then minus 2 outside of square root / square root x^3 - 8 ( 8 is not under the root)

x--> 4

Re: Evaluating limits using change of variable/ variable substitution

Use the difference of cubes formula to reduce each fraction

For the first one we get

This will reduce out with the factor of the numerator and now the function is continuous so you can just evaluate at x=27

Re: Evaluating limits using change of variable/ variable substitution

Quote:

Originally Posted by

**Bri22** Hi there! I am currently in grade 12, studying calculus 30 which is just calculus. I have a question about the above topic posted. One contains roots and I'm not sure exactly how to solve it. Any help would be great!

1) lim ( X^1/3 - 3) / (x - 27)

X-->27

2) lim. (square root of x then minus 2 outside of square root / square root x^3 - 8 ( 8 is not under the root)

x--> 4