Question

Find $$\lim _{h \rightarrow 0} \frac{f(2+h)-f(2)}{h}$$ $$f(x)=\sqrt{x}$$

   Find
$$\lim _{h \rightarrow 0} \frac{f(2+h)-f(2)}{h}$$
$$f(x)=\sqrt{x}$$

Contemporary Precalculus

Contemporary Precalculus

Thomas W.… 5th Edition

Chapter 13, Problem 44

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Solved by Expert Amy Jiang

07/16/2020

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Find $$\lim _{h \rightarrow 0} \frac{f(2+h)-f(2)}{h}$$ $$f(x)=\sqrt{x}$$

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Key Concepts

Rationalization

Rationalization is an algebraic technique used to simplify expressions involving radicals. In the context of evaluating limits, particularly those that result in indeterminate forms, multiplying by the conjugate can help eliminate radicals and make the limit evaluation more straightforward.

Limit

The concept of a limit is central in calculus and involves determining the value that a function approaches as the input approaches a particular point. In problems involving derivatives, limits are used to rigorously define instantaneous rates of change by considering the behavior of functions as the increment approaches zero.

Derivative

A derivative represents the instantaneous rate of change of a function with respect to one of its variables. It is defined as the limit of the difference quotient as the increment tends to zero, providing a precise way to measure how a function value changes as its input changes infinitesimally.

Difference Quotient

This concept is a formula that computes the average rate of change of a function over an interval and forms the basis of the derivative. By taking the limit of the difference quotient as the interval becomes infinitesimally small, one obtains the derivative of the function.

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