NATURE.M said:Homework Statement
lim (cubicsquareroot(x) - 2)/(x-8)
x→8
Homework Equations
The Attempt at a Solution
I obtained 1/12 as my final answer, after changing the variable since its in indeterminate form.
..let p=cubicsquareroot(x), then as x→8, p→2
then, p^3=x
Using this logic I obtained 1/12.
Is this correct ?
PrashntS said:Precisely, Although It'd be nicer if you had done some substitutions.. Yeah is correct!
SammyS said:What's a "cubicsquareroot" ?
L' Hopital's Rule is not needed in this problem.PrashntS said:My bad! you have! And when you reach L'Hopital's rule, revisit these questions..
Evaluating a limit means finding the value that a function approaches as the independent variable approaches a specific value or as it gets infinitely close to that value. It helps to determine the behavior of a function at a particular point.
To evaluate a limit algebraically, you can try to simplify the function by factoring, canceling out common terms, or using algebraic manipulations. You can also use the properties of limits, such as the sum, difference, product, and quotient rules, to evaluate the limit.
Yes, it is possible to evaluate a limit even if the function is undefined at that point. However, the limit may not exist in this case. It is important to consider the one-sided limits from both the left and right sides to determine the existence and value of the limit.
A one-sided limit is the value that a function approaches as the independent variable approaches a specific value from only one direction (either left or right). On the other hand, a two-sided limit is the value that a function approaches as the independent variable approaches a specific value from both the left and right sides. In other words, a two-sided limit takes into account the behavior of the function from both directions, while a one-sided limit only considers one direction.
Evaluating limits is important because it helps to understand the behavior of a function at a particular point. It can also help to determine if a function is continuous at a specific point and can be used to solve various problems in mathematics, physics, engineering, and other fields. Additionally, it is a fundamental concept in calculus and is necessary for understanding more advanced topics such as derivatives and integrals.