Definition of the Tangent Line
The tangent line is a fundamental concept in calculus and geometry, serving as a crucial tool for understanding the behavior of functions and curves at specific points. In mathematics, the tangent line to a curve at a given point is defined as the straight line that just touches the curve at that point, sharing its slope. This line represents the best linear approximation to the curve near the chosen point, allowing for precise analysis of the curve's behavior in the vicinity of that point. The concept of the tangent line finds widespread applications across various fields, including physics, engineering, and computer science.
Questions
- Find the equation of tangent parallel to the secant joining the points on the curve #y=x^2# at #x=-1# and #x=2#?
- Are there any numbers for which the expression #(8x^4+9)/(9x^2+18x)# undefined?
- How do I find the secant line through two points?
- How do I find the tangent line of a function?
- How do I find the tangent line of #y=x^2# at its vertex?
- How do I draw tangent lines?
- What is the tangent line of a parabola at its vertex?
- How can I tell if a line is tangent to a circle?
- What is a secant line?
- What is the formula for the slope of a secant line?
- Why are the tangents for 90 and 270 degrees undefined?
- How do you find the equation of the tangent to the curve #y = 2 - sin^2 x# at the point where x = pi/6?
- Two tangents to the parabola #y=1-x^2# intersect at point #(2,0)#. Find the coordinates of points on parabola on which these are tangents?
- Find the condition under which the line #xcosalpha+ysinalpha=p# will be a tangent to the conic #3x^2+4y^2=5#?
- What is the equation of the tangent plane to the graph of # g(x,y)= e^{-y}sin(x)+e^{-2y} # at #(0,0,1)#...? Thanks :)
- How to find the value of a?
- What is a tangent line?
- What are common mistakes students make with tangent lines?