Equation of the tangent line at (0, pi/2)

In summary, when solving for the equation of the tangent line to the given formula where y = pi/2 when x = 0, the slope is found to be undefined. This means that the tangent line is a vertical line and the equation of this line through the point (0, pi/2) is x = 0.
  • #1
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Find the equation for the line that is tangent to the given formula if y = pi/2 when x = 0

Homework Equations



(x+1)dy - [(1/2)secycscy]dx = 0

The Attempt at a Solution



I tried to do this, and I got that

dy/dx = 1 / (0*0), which is infinity.

So...

y = [tex]\infty[/tex]?
 
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  • #2
OK, so the slope is undefined. What kind of line has a slope that's undefined?
 
  • #3
So it's a vertical line and no longer a function. That's the answer?
 
  • #4
Your original problem was to find the tangent line. Nothing was said about being a function. What is the equation of the vertical line through (0, pi/2)?
 

FAQ: Equation of the tangent line at (0, pi/2)

What is a tangent line?

A tangent line is a line that touches a curve at only one point, called the point of tangency. It represents the instantaneous rate of change of the curve at that point.

How do you find the tangent line to a curve?

To find the tangent line to a curve, you need to calculate the derivative of the curve at the point of interest. This derivative represents the slope of the tangent line. Then, you can use the point-slope formula to write the equation of the tangent line.

Why is the tangent line important?

The tangent line is important because it helps us understand the behavior of a curve at a specific point. It can be used to approximate the curve's values and make predictions. It also plays a crucial role in the study of calculus and its applications in various fields of science and engineering.

What are some real-life applications of finding tangent lines?

Finding tangent lines has many practical applications, such as in physics to calculate instantaneous velocity or acceleration, in economics to analyze demand and supply curves, and in engineering to design optimal routes for vehicles or pipes.

Are there any limitations to finding tangent lines?

Yes, there are limitations to finding tangent lines. It only provides an approximation of the curve's behavior at a specific point and cannot accurately represent the entire curve. Additionally, some curves may not have a well-defined tangent line at certain points, such as a sharp corner or a vertical tangent.

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