The limit represents the derivative of some role f(x) at some number a. Uncover f and a.

You are watching: The limit represents the derivative of some function f at some number a. state such an f and a.

lim (h->0) of ((7+h)^2-49)/h

 


Who room the experts?Our certified Educators are real professors, teachers, and scholars who usage their scholastic expertise come tackle your toughest questions. Educators go through a rigorous application process, and also every answer they send is the review by our in-house editorial team.


*

expect that the duty is `f(x)=x^2` and `a = 7` .

You need to discover the derivative the the role at x=a=7, hence, using the limit an interpretation of derivatives yields:

`f"(x) = lim_(h-gt0) (f(x+h)-f(x))/h`

`f"(x) = lim_(h-gt0) ((x+h)^2-x^2)/h`

Expanding the binomial yields:

`f"(x) = lim_(h-gt0) (x^2 + 2xh + h^2...


Start her 48-hour free trial to unlock this answer and also thousands more. Gain londonchinatown.org ad-free and also cancel anytime.


Suppose the the role is `f(x)=x^2` and also `a = 7` .

You need to discover the derivative the the role at x=a=7, hence, utilizing the limit meaning of derivatives yields:

`f"(x) = lim_(h-gt0) (f(x+h)-f(x))/h`

`f"(x) = lim_(h-gt0) ((x+h)^2-x^2)/h`

Expanding the binomial yields:

`f"(x) = lim_(h-gt0) (x^2 + 2xh + h^2 - x^2)/h`

Reducing choose terms yields:

`f"(x) = lim_(h-gt0) (2xh + h^2)/h`

Factoring out h yields:

`f"(x) = lim_(h-gt0) h(2x + h)/h =gt f"(x) = lim_(h-gt0) (2x + h) = 2x`

Equating `((x+h)^2-x^2)/h` and also `((7+h)^2-49)/h` yields x + h = 7 + h and `x^2 = 49` .

Notice that het relations provides `x_(1,2) = +-7` however the an initial relation x + h = 7 + h excludes the worth -7, hence x = 7.

Hence, evaluating the function yields the `f(x) = x^2` and also a=7 => f"(7) = 14.

See more: The Problem Of Urban Sprawl Is A Possible Cause Of Deforestation


approved by londonchinatown.org Editorial Team

Ask a Question

ask a question
Submit concern

Popular Questions


see all

Related Questions

Browse all
Math

recent answer posted October 03, 2011 in ~ 2:12:01 afternoon


This limit represents the derivative the some role f at some number a. State this f and a. Lim h->0 <(4th source of)(16+h)-2>/h a=? f=?


1 education answer

Math

recent answer post February 18, 2012 in ~ 12:06:30 pm


The limitlim (h->0) that (sqrt(81+h)-9)/hrepresents the derivative of some role f(x) at part number a. Find f and also a


1 educator answer

Math

recent answer post November 15, 2010 in ~ 1:46:06 am


advice lim / h together h---> 0


2 educator answers

Math

recent answer post February 17, 2010 in ~ 12:21:51 pm


use the 4 step procedure to uncover the derivative the f(x) whereby f'(x) = lim /h (the lim is h to 0) :f(x) = 1 / 4x-3


2 educator answers

Math

latest answer posted April 18, 2012 in ~ 6:56:41 to be


discover the derivative that f(x)= x^2 + 5^x using lim h-->0 f(x+h)-f(x)/h


1 educator answer
londonchinatown.org will help you with any kind of book or any kind of question. Ours summaries and also analyses space written by experts, and also your concerns are answered by actual teachers.

join londonchinatown.org


use to it is in an education

Recommended

More


©2021 londonchinatown.org, Inc. All rights Reserved