RD Sharma Class 12 Solutions Chapter 16 - Tangents and Normals (Ex 16.1) Exercise 16.1 - Free PDF
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Tangents are lines that only meet a given curve and at the point of contact, their normal is a line perpendicular to it. One explanation of why tangents are so important is that they give slopes of straight lines. Normal lines are also important when dealing with orientation questions, especially in higher dimensions. The RD Sharma Class 12 Chapter 16 Solutions will give a basic understanding of Tangents and Normals along with the important questions asked in board exams.
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FAQs on RD Sharma Class 12 Solutions Chapter 16 - Tangents and Normals (Ex 16.1) Exercise 16.1
1. What is a tangent?
A tangent at a point on a curve is a straight line that touches the curve at that point and has the same slope as the curve's gradient/derivative. You may derive how to obtain the equation of the tangent to the curve at any point from the definition. The equation of the tangent to this curve at x = x0, given a function y = f(x), may be calculated as follows:
Find the curve's gradient/derivative at the point x = x0: To do so, one must first calculate dydxx=x0. In the same way that the slope of a straight line is called m, we'll call this value m.
Find the equation of the straight line with slope m that passes through the point (x0, y(x0) y–y1x–x1=m is a simple formula that can be obtained.
2. What is normal?
A straight line that meets the curve at a point on the curve and is perpendicular to the tangent at that point is called a normal. If n is its slope, and m is the slope of the tangent at that point or the value of the gradient/derivative at that point, we obtain mn = -1. Finding the normal to a given curve y = f(x) at a point x = x0 involves the following steps:
Find the curve's gradient/derivative at the point x = x0: This first step is identical to the approach for determining the equation of the tangent to the curve, i.e. m = dydxx=x
Determine the normal slope 'n': We have n=1m since the normal is perpendicular to the tangent.
3. How can the tangent be found and what is a gradient?
The tangent can be found by following these steps:
Draw the tangent line as well as the function.
To calculate the equation for the tangent line's slope, use the first derivative.
Enter the x value for the point you're looking into.
Write the tangent line's equation in point-slope form.
Finally, check the equation on the graph for accuracy.
The steepness of a graph at any point is referred to as the gradient. The gradient of the graph at any point is referred to as slope. As a result, both can be considered identical.
4. What are the applications of Tangent and Normal?
The Applications Of Tangent Are:
If we are driving around a corner and hit something slick on the road (oil, ice, water, or loose gravel) and our automobile starts to skid, it will continue in a tangent to the curve direction.
Similarly, if we hold a ball in our hands and swing it circularly before releasing it, the ball will fly out in a tangent to the circle of motion.
The Applications Of Normal Are:
When you are speeding around a circular track in an automobile, the force pushing you outwards is proportional to the curve of the road. Surprisingly, the force that propels you around the corner is directed normal to the circle, towards the circle's centre.
At each point where the spoke meets with the centre, the spokes of a wheel are aligned normal to the circular shape of the wheel.
5. How to prepare for the chapter Tangents and Normals?
Students have a strong foundation to prepare for the chapter - tangents and normal. Students need to have a great base to build further knowledge on the chapter. Students should grasp concepts like tangents, normal, applications of a tangent, applications of normal, gradient, curve, derivative, slope etc. Students should also prepare for the chapter - tangents and normal by solving sample papers related to the chapter, as practice will help them more. To get free study materials, people can visit the Vedantu app and website.