# How do you find the equation for the tangent line for #y=1/x# at #x=1#?

By signing up, you agree to our Terms of Service and Privacy Policy

You can alternatively use the Newton Approximation Method, which is:

or

By signing up, you agree to our Terms of Service and Privacy Policy

To find the equation for the tangent line of the function y = 1/x at x = 1, we need to determine the slope of the tangent line at that point and then use the point-slope form of a linear equation.

First, we find the derivative of the function y = 1/x using the power rule for differentiation. The derivative of 1/x is -1/x^2.

Next, we substitute x = 1 into the derivative to find the slope of the tangent line at x = 1. Plugging in x = 1, we get -1/1^2 = -1.

Now, we have the slope of the tangent line, which is -1. We also have the point (1, 1) since x = 1 is the point of tangency.

Using the point-slope form of a linear equation, y - y1 = m(x - x1), we substitute the values we have:

y - 1 = -1(x - 1)

Simplifying, we get:

y - 1 = -x + 1

Rearranging the equation, we obtain the equation for the tangent line:

y = -x + 2

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the slope of the line tangent to the graph of #y=ln(x^2)# at #x=e^2#?
- What is the equation of the tangent line of #f(x)=(2x)/(x+1)^2 # at #x=0#?
- Consider the circle of radius 5 centered at (0,0), how do you find an equation of the line tangent to the circle at the point (3,4)?
- Using the limit definition, how do you differentiate #f(x)=x^2-4x+23#?
- How do you find the equations for the tangent plane to the surface #x=y(2z-3)# through #(4, 4, 2)#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7