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Use continuity to evaluate the limit.
$ \displaystyle \lim_{x \to 2} x \sqrt{20 - x^2} $
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Calculus 1 / AB
Chapter 2
Limits and Derivatives
Section 5
Continuity
Limits
Derivatives
Missouri State University
Harvey Mudd College
University of Michigan - Ann Arbor
Boston College
Lectures
04:40
In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.
In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
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This is problem thirty five Stewart Calculus, eighth edition, Section two point five. Use continuity to evaluate the limit. A limit, his expertise to X multiplied by the square root of the quantity twenty minus X squared Here to the rain to recall we have the definition of continuity. Um, that if a function of its continuous a point Okay, then the limit is expert Jesse. There was a function of is equal to f A A. If we look at this function, you see that it is eh? Combination. The product of two continuous functions we have am xs one function. The square root is another function. And then within its where we also have a polynomial which is continuous on its domain. And we have no domain restrictions, especially you. X equals a rex equals two. So because we know this function is continuous, the solution to this limit will be the the foot dysfunction evaluated it too. So two times the square root twenty minutes to squared, which is two times the square root of twenty minutes for or sixteen. Just two teams for we're just going to be eight, and that is our final answer.
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