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Compute the indicated limit.(a) $\lim _{x \rightarrow \infty} \frac{2 x^{8}+3 x^{5}+7 x}{5 x^{14}+7 x^{9}+2}$(b) $\lim _{x \rightarrow-\infty} \frac{2 x^{8}+3 x^{5}+7 x}{5 x^{14}+7 x^{9}+2}$

(a) 0(b) 0

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 4

Limits at Infinity, Infinite Limits and Asymptotes

Derivatives

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

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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Hello. We have to compute this limit so we can write it like this limit extends to infinity. B will take. We will take extra. The power eight each comin from the narrator It will be two plus three by extra the power of three plus seven by X 20 power of seven and from the drowned Later we will take to the power 14. We will take common actually our 14 from denominators that we leave five plus seven upon actually power of five plus two by actually power 14 Now we will put the limit. Okay, so it will be went up on extra the power six two plus zero Because it is one by X cube it will also review and upon five plus Thank you. Five plus zero plus zero. And it is It will be close to that. And from here we can try. We will put the value of the limit. So it will be in 50 power of six. So ban by inflatable b zero I hope you understood. Thank you. This is the same function so we can limit extra. The power extends to the Madison pretty and one by X to the power six I wasn't two plus three by X Cubed plus seven by extra The governor of seven upon five plus seven by extra The power five plus 25 x to the power of 14. Okay, this is that we function. We can died in that place of X We can put in medicine 50 So it will be minus 7 50 Power of six to play 00 It is five plus zero plus zero. So there will be calls to ban upon infinity will be zero That is 25. That is the cost to zero. I hope you understand. Thank you. Mhm.

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