What happens if a limit is 0 0

Integration Techniques A. Applications Of Integration A. Understanding Data A. Data Basics What is Data? Probability Basics A. Common Probability Distributions A. Inference Testing A. Regression Processes A. Misfit Math About Mr. Math Contact Mr. Book a Session! Contact Mr. Vocab FYI:. Fun Fact:. You Should Know. Pro Tip. We only need prove it with limits to answer the question. Let's start with the left-side limit. Since the one-sided limits do not agree, the two-sided limit doesn't exist.

As such, our procedure will be to look at each one-sided limit, starting with the left side. As we stated earlier, the procedure in that case will always be to try and get some factors to cancel. Let's factor each the numerator and denominator and see what happens.

Let's factor and cancel. This one requires us to pull out a small trick from Algebra Two: the numerator is a sum of cubes, which has a special presumably memorized form. When working on a problem of this type with polynomial type variable expressions in the numerator, the general procedure will be to expand if possible and combine like terms.

The rest will take care of itself. The secret for rational function type difference quotient problems is to get a common denominator. The rest will fall into place. Lesson Metrics At the top of the lesson, you can see the lesson title, as well as the DNA of Math path to see how it fits into the big picture.

Key Lesson Sections Headlines - Every lesson is subdivided into mini sections that help you go from "no clue" to "pro, dude". Perils and Pitfalls - common mistakes to avoid. The value that the function takes at the limit poit is irrelevant to compute the limit.

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Git Gud Student Student 2 2 gold badges 7 7 silver badges 18 18 bronze badges. This is probably a homework problem, so look at the numerator for a hint.

Add a comment. Active Oldest Votes. Sammy Black Sammy Black 15k 2 2 gold badges 25 25 silver badges 43 43 bronze badges. Chain rule. An unnoticed composition Two young mathematicians discuss the chain rule. The chain rule Here we compute derivatives of compositions of functions. Derivatives of trigonometric functions We use the chain rule to unleash the derivatives of the trigonometric functions.

Higher order derivatives and graphs. Rates of rates Two young mathematicians look at graph of a function, its first derivative, and its second derivative. Higher order derivatives and graphs Here we make a connection between a graph of a function and its derivative and higher order derivatives.

Concavity Here we examine what the second derivative tells us about the geometry of functions. Position, velocity, and acceleration Here we discuss how position, velocity, and acceleration relate to higher derivatives. Standard form Two young mathematicians discuss the standard form of a line.

Implicit differentiation In this section we differentiate equations that contain more than one variable on one side. Derivatives of inverse exponential functions We derive the derivatives of inverse exponential functions using implicit differentiation. Logarithmic differentiation. Multiplication to addition Two young mathematicians think about derivatives and logarithms. Logarithmic differentiation We use logarithms to help us differentiate.

Derivatives of inverse functions. We can figure it out Two young mathematicians discuss the derivative of inverse functions. Derivatives of inverse trigonometric functions We derive the derivatives of inverse trigonometric functions using implicit differentiation.

The Inverse Function Theorem We see the theoretical underpinning of finding the derivative of an inverse function at a point. More than one rate. A changing circle Two young mathematicians discuss a circle that is changing. More than one rate Here we work abstract related rates problems. Applied related rates. Pizza and calculus, so cheesy Two young mathematicians discuss tossing pizza dough.

Applied related rates We solve related rates problems in context. Maximums and minimums. More coffee Two young mathematicians witness the perils of drinking too much coffee.

Maximums and minimums We use derivatives to help locate extrema. Concepts of graphing functions. Two young mathematicians discuss how to sketch the graphs of functions. Concepts of graphing functions We use the language of calculus to describe graphs of functions.

Computations for graphing functions. Wanted: graphing procedure Two young mathematicians discuss how to sketch the graphs of functions. Computations for graphing functions We will give some general guidelines for sketching the plot of a function.

Mean Value Theorem. The Extreme Value Theorem We examine a fact about continuous functions. The Mean Value Theorem Here we see a key theorem of calculus. Replacing curves with lines Two young mathematicians discuss linear approximation.

Explanation of the product and chain rules We give explanation for the product rule and chain rule. A mysterious formula Two young mathematicians discuss optimization from an abstract point of view.

Basic optimization Now we put our optimization skills to work. Applied optimization. Volumes of aluminum cans Two young mathematicians discuss optimizing aluminum cans. Applied optimization Now we put our optimization skills to work. A limitless dialogue Two young mathematicians consider a way to compute limits using derivatives.

Basic antiderivatives We introduce antiderivatives. Falling objects We study a special type of differential equation. Approximating the area under a curve. What is area? Two young mathematicians discuss the idea of area. Introduction to sigma notation We introduce sigma notation.

Approximating area with rectangles We introduce the basic idea of using rectangles to approximate the area under a curve. Definite integrals. Computing areas Two young mathematicians discuss cutting up areas. The definite integral Definite integrals compute net area. Antiderivatives and area. Meaning of multiplication A dialogue where students discuss multiplication.

Relating velocity, displacement, antiderivatives and areas We give an alternative interpretation of the definite integral and make a connection between areas and antiderivatives. First Fundamental Theorem of Calculus.