- #1
synergix
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Homework Statement
lim e3/(2-x)
x->2+
The Attempt at a Solution
I can't seem to get started on this one.
synergix said:e will be raised to a larger and larger negative number as x approaches 2+ and so the limit will approach 0.
A natural exponential function is a mathematical function of the form f(x) = e^x, where e is a mathematical constant approximately equal to 2.71828. It is a special type of exponential function that is commonly used in mathematics and science.
Natural exponential functions have several important properties, including a positive y-intercept, a continuous and differentiable curve, and an inverse function of ln(x). They also have the unique property that their derivative is equal to the function itself.
Limits involving natural exponential functions are evaluated using the rules of calculus, specifically the limit definition of the derivative. This involves taking the limit of the function as x approaches a certain value, and then using algebraic manipulation and substitution to simplify the expression and find the limit.
Limits involving natural exponential functions are used in many fields, including physics, chemistry, and finance. For example, they can be used to model population growth, radioactive decay, and compound interest.
Yes, there are several special techniques that can be used to evaluate limits involving natural exponential functions. One common technique is to rewrite the function in terms of its inverse, ln(x), and then use properties of ln(x) to simplify the expression. Another technique is to use L'Hopital's rule, which involves taking the derivative of both the numerator and denominator of the function and then taking the limit again.