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Using Exercise $69,$ prove that $x^{5}+x-5=0$ has a root between $x=1$ and $x=2.$

$f(0) 60, f(2) > 0$

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.

02:26

If x= 2+ root 5. Prove tha…

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Show that the equation $x^…

01:17

Show that the equation $6 …

01:09

01:32

03:06

In Exercises $67-70$ , use…

01:04

Show that the equation $1+…

02:43

Show that the cquation $6 …

02:06

Finding a Solution In Exer…

01:11

Prove that the equation $\…

03:16

Prove that the equation $x…

01:51

So if X equals X to the power five plus. So clearly, clearly F is continuous for continuous. Oh, what all, really? X. No, F G do equal zero to the power five plus. Zero equals zero to less than come on. No, F one Equal 1 to the power five plus plus one, Which is equal to two greater than one. So hence from hands from intermediate intermediate value theorem value your um, there exist a number. There exist A number in Jiro to one. A number mm hmm. Jiro to search there so that, mm hmm. See

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