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Find the indicated limit.$$f(x)=7 x^{2}+2 h-3, \text { determine }(a) \lim _{h \rightarrow 0} f(x)(b) \lim _{x \rightarrow 0} f(x)$$

(a) $7 x^{2}-3$(b) $2 h-3$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 3

Limits and Continuity

Derivatives

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Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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00:51

in problem 14. We have to. Fine. We have to deter mine the limit off the U. N. Function. We have to determine the limit off the given function. If off axis goal to seven X squared plus to edge minus three. In a part off this problem, we have to find the limit. If all of eggs is it projects toe zero. So we have limit. It approaches to zero off. Seven X care plus two edge minus three. Here X is constant. The variable is edge India, for we will replaced edge by zero when we're blind. The limit. So we have seven x a pair plus two into zero minus three which is equal to seven x squared minus two times 00 So we have minus three in part. Be off this problem. We had to find the limit off in full of eggs when X approaches to zero. So we have limit as extends to zero. The given function is seven x a care less to edge minus three. After applying limits, we have seven into zero all scared plus to EJ minus three. Seven times zero is zero. So we have finally we have to edge minus three, which is the required limit for the human function as X approaches to zero

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