Solving Calculus Problems: Asymptotes, Normal Lines, and Average Rate of Change

Thread starter jai6638
Start date Aug 28, 2005
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How do we arrive at the conclusion to find the gradient perpendicular to the tangent.Ok, so we know that the tangent line has one gradient at that point. But we want the normal line that is perpendicular to that line. To do that, we have to do a couple of things:1. Find the tangent (using differentiation).2. Find the perpendicular gradient to that tangent.3. Put it all into the second equation of a straight line (y - y1 = m (x - x1)).We're not really finding the gradient perpendicular to a point, that doesn't make any sense. We find the gradient perpendicular to the tangent, which is a line.The Bob (2004 ©)In

Aug 29, 2005

Homework Helper

If you know A, a and c, you can use the law of sines:

[tex]\frac{{\sin A}}{a} = \frac{{\sin B}}{b} = \frac{{\sin C}}{c}[/tex]

<h2>What is an asymptote?</h2><p>An asymptote is a line that a curve approaches but never touches. This means that as the curve gets closer and closer to the line, it will never actually intersect with it.</p><h2>How do you find the equation of a normal line?</h2><p>To find the equation of a normal line, you first need to find the slope of the tangent line at the point of interest. Then, take the negative reciprocal of that slope to find the slope of the normal line. Finally, use the point-slope form of a line to find the equation of the normal line.</p><h2>What is the average rate of change?</h2><p>The average rate of change is the average rate at which a quantity changes over a specific interval. It is calculated by finding the difference between the final and initial values of the quantity and dividing by the change in time or x-values.</p><h2>How do you find the vertical asymptote of a function?</h2><p>The vertical asymptote of a function is a vertical line on the graph where the function approaches infinity or negative infinity. To find the vertical asymptote, set the denominator of the function equal to zero and solve for the x-value. This will give you the equation of the vertical asymptote.</p><h2>What is the difference between a horizontal and a vertical asymptote?</h2><p>A horizontal asymptote is a horizontal line on the graph where the function approaches a specific value (usually zero) as x approaches infinity or negative infinity. A vertical asymptote, on the other hand, is a vertical line where the function approaches infinity or negative infinity as x approaches a specific value. In other words, a horizontal asymptote is a limit of the function as x goes to infinity, while a vertical asymptote is a limit of the function as x approaches a specific value.</p>

What is an asymptote?

An asymptote is a line that a curve approaches but never touches. This means that as the curve gets closer and closer to the line, it will never actually intersect with it.

How do you find the equation of a normal line?

To find the equation of a normal line, you first need to find the slope of the tangent line at the point of interest. Then, take the negative reciprocal of that slope to find the slope of the normal line. Finally, use the point-slope form of a line to find the equation of the normal line.

What is the average rate of change?

The average rate of change is the average rate at which a quantity changes over a specific interval. It is calculated by finding the difference between the final and initial values of the quantity and dividing by the change in time or x-values.

How do you find the vertical asymptote of a function?

The vertical asymptote of a function is a vertical line on the graph where the function approaches infinity or negative infinity. To find the vertical asymptote, set the denominator of the function equal to zero and solve for the x-value. This will give you the equation of the vertical asymptote.

What is the difference between a horizontal and a vertical asymptote?

A horizontal asymptote is a horizontal line on the graph where the function approaches a specific value (usually zero) as x approaches infinity or negative infinity. A vertical asymptote, on the other hand, is a vertical line where the function approaches infinity or negative infinity as x approaches a specific value. In other words, a horizontal asymptote is a limit of the function as x goes to infinity, while a vertical asymptote is a limit of the function as x approaches a specific value.