D H said:Your use of parentheses doesn't make sense. Do you mean
[tex]f(x) = \sqrt{e^x+3}[/tex]
[tex]f(x) = \sqrt{e^x} + 3[/tex]
[tex]f(x) = {\sqrt e}^{x + 3}[/tex]
[tex]f(x) = {\sqrt e}^x + 3 [/tex]
Or even yet something else?
D H said:You could have written it as f(x)=sqrt(e^x+3) and that would have been fine.
f(x)=(sqrt e^x+3) was pretty much meaningless.
What is the derivative of f(x) at x=0?
Linear approximation is a method used in calculus to approximate the value of a function at a certain point by using the tangent line at that point. It is a useful tool for estimating values of functions that are difficult to calculate directly.
For square root functions, linear approximation involves finding the equation of the tangent line at a certain point on the function and using that line to approximate the value of the function at that point. This is helpful when finding the square root of a number with a non-perfect square, as it provides a close estimate.
Yes, linear approximation can be used for tangent functions. In this case, the tangent line is used to approximate the value of the function at a certain point. This is particularly useful for finding the value of tangent functions at angles that are not easily calculable.
For e^x functions, linear approximation involves using the tangent line at a point to approximate the value of the function at that point. This is helpful when trying to find the value of e^x at a non-integer value of x, as it provides a close estimate.
Linear approximation is only accurate for small intervals around the point of approximation. The further away the point is from the point of approximation, the less accurate the estimate will be. Additionally, it can only be used for functions that are differentiable at the point of approximation.