We offer various automated calculus tutorials. We cover the following topics: limits, continuity, derivatives and antiderivatives, and applications of integrals. Our tutorials are automated and interactive, feel free to use our application when preparing for exams or doing homework assignments.
The limit of a function at a point is the value that the function approaches as the input approaches that point.
Suppose f(x) is defined when x is near the number a. (This means that f is defined on some open interval that contains a, except possibly at x=a itself.) Then we write
and say "the limit of f(x), as x approaches a, equals L" if we can make the values of f(x) arbitrarily close to L (as close to L as we like) x to be sufficiently close to a (on either side of a) but not equal to a.
In this video, we learn how to compute the limit of an irrational function using the conjugate expression of the radical expression. The functions is undefined at x = 1, but if we make this statement and no other, we give a very incomplete picture of how each function behaves in the vicinity of x = a. To express the behavior of each graph in the vicinity of 1 more completely, we need to introduce the concept of a limit.
Problem-Solving Strategy: Calculating a Limit When f(x)/g(x) has the Indeterminate Form 0/0
1. First, we need to make sure that our function has the appropriate form and cannot be evaluated immediately
using the limit laws.
2. We then need to find a function that is equal to h(x) = f (x)/g(x) for all x ≠ a over some interval containing
a. To do this, we may need to try one or more of the following steps:
a. If f (x) and g(x) are polynomials, we should factor each function and cancel out any common factors.
b. If the numerator or denominator contains a difference involving a square root, we should try
multiplying the numerator and denominator by the conjugate of the expression involving the square
root.
c. If f (x)/g(x) is a complex fraction, we begin by simplifying it.
3. Last, we apply the limit laws.
This limit problem particularly uses conjugate expression to simplify the radical term.
Негізгі бет Limit with a radical term in the denominator (-2+x)/(sqrt(-3+x^2)-1) at x=2
Пікірлер