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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
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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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. dy dt 2 3 4 S I = = lim At 0 = lim At-0 = lim At 0 = lim lim At→0 - f(t+At)-f(t) At 72. 2 t+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) = and f(t) = 2/ t 2 t+Ãt Combine fractions in numerator. Divide out common factor of At. Simplify. Evaluate limit as At → 0.
Transcribed Image Text:1. dy dt 2 3 4 S I = = lim At 0 = lim At-0 = lim At 0 = lim lim At→0 - f(t+At)-f(t) At 72. 2 t+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) = and f(t) = 2/ t 2 t+Ãt Combine fractions in numerator. Divide out common factor of At. Simplify. Evaluate limit as At → 0.
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