# How do you find the equation of the tangent line to the graph of f(x) at given point if #f(x)= sqrt(x+1))# at (0,1)?

graph{(y-sqrt(x+1))(y-1/2x-1)=0 [-1.84, 2.487, -0.099, 2.064]}

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To find the equation of the tangent line to the graph of f(x) at the given point (0,1), we can use the concept of the derivative.

First, we need to find the derivative of f(x). The derivative of f(x) = sqrt(x+1) can be found using the power rule of differentiation.

The derivative of f(x) = sqrt(x+1) is f'(x) = 1 / (2 * sqrt(x+1)).

Next, we substitute x = 0 into the derivative to find the slope of the tangent line at the point (0,1).

f'(0) = 1 / (2 * sqrt(0+1)) = 1 / (2 * sqrt(1)) = 1 / (2 * 1) = 1/2.

So, the slope of the tangent line at (0,1) is 1/2.

Now, we can use the point-slope form of a linear equation to find the equation of the tangent line.

Using the point-slope form, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we substitute the values.

y - 1 = (1/2)(x - 0).

Simplifying, we get y - 1 = (1/2)x.

Finally, we can rewrite the equation in slope-intercept form, y = mx + b, where b is the y-intercept.

y = (1/2)x + 1.

Therefore, the equation of the tangent line to the graph of f(x) = sqrt(x+1) at the point (0,1) is y = (1/2)x + 1.

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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.

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