I am needing help with simplifying the fraction between step 3-4. How do I get from step 3 (combine fract. in num.) to step 4 (div. out common factor of delta t) algabraecally? I've tried working out the problem several times and keep getting stumped at that part. 1. dydt234SI== limAt 0=limAt-0=limAt 0= limlimAt→0-f(t+At)-f(t)At72.2t+AtAt2-2 AtAt→0 At (t) (t+At)-t2t-2(t+At)t(t+At)At-2t(t+At)Definition of derivativef(t + At) = and f(t) = 2/t2t+ÃtCombine fractions in numerator.Divide out common factor of At.Simplify.Evaluate limit as At → 0.

I am going to solve the problem by using some simple calculus to get the required result of the…

1. dy dt 2 3 14 S I = lim At→0 =lim At 0 = lim - At→0 = lim lim At→0 f(t+At)-f(t) At 2 -7. 2 +At At 2 -2 At At 0 At (t) (t+At) t 2t-2(t+At) t(t+At) At -2 t(t+At) Definition of derivative f(t + At) = t+ and f(t) = ²/ 2 t+At t Combine fractions in numerator. Divide out common factor of At. Simplify. Evaluate limit as At → 0.

1. dy dt 2 3 14 S I = lim At→0 =lim At 0 = lim - At→0 = lim lim At→0 f(t+At)-f(t) At 2 -7. 2 +At At 2 -2 At At 0 At (t) (t+At) t 2t-2(t+At) t(t+At) At -2 t(t+At) Definition of derivative f(t + At) = t+ and f(t) = ²/ 2 t+At t Combine fractions in numerator. Divide out common factor of At. Simplify. Evaluate limit as At → 0.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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