Find an equation of the tangent line to the curve, f(x) =1x2+ 1at (0,1) by using the limitdefinition of the derivative. (Dont use Derivative Rules)

y = 1.

Step-by-step explanation:

f(x) = x^2 + 1

We know that:

replacing the function, we get:

Now we can simplify this to:

and solving the quotient, we get:

then f'(x) = 2*x

And we want the equation for the tangent line at (0, 1)

The slope of that line will be:

f'(0) = 2*0 = 0

So this is a horizontal line, of the type y = a

And we know that this line must pass through the point (0, 1)

so we must have y = 1.

Then the equation of the tangent line to f(x) at the point (0, 1) is:

y = 1.