MATH 1910 If high school precalculus and ACT math of at least 26 contact 694
MATH 1910 If high school precalculus and ACT math of at least 26 contact 694 MATH 1910
pellissippi state community college
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This 0 page Class Notes was uploaded by Brown Lowe on Sunday November 1, 2015. The Class Notes belongs to MATH 1910 at pellissippi state community college taught by Jon Lamb in Fall. Since its upload, it has received 23 views. For similar materials see /class/232964/math-1910-pellissippi-state-community-college in Mathematics (M) at pellissippi state community college.
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Date Created: 11/01/15
10 Sectinn 22 The Limit at a Functinn Ex What do the yrvalues ofthe graph of fx 5 approaeh as the xrvalues approaeh m V ook at atable ul turl u rt as x gt 0 use ASK mode ZOOMZDEC l as x 90 But the fuhetloh ls not de ned at x 0 Look at the graph wrth the axes tumed off 24 FORMAT AxesOfO 39 You eau barely tell but there ls ahole m the graph at x 0 The fuhetloh ls hot deflnedthere DEFINITION OF LIMIT We wnte llmx L and say thallmltofx as rapproaehesaequalsLquot Ha lf we eau make the values of x arbrtrauly elose to L as elose to L as we llke by taluhg x to be sumelehtly elose to equal a mtertded valuequot value approaehes 0 does equal 1 beeause that ls the lntended yrvalue the graph approaehs A sth So l 5 A llrh 1 xgt x xgt APPLICATIONS OF DIFFERENTIATION 41 RELATED RATES 2 Compute the rate of change of one quantity in terms of the rate of change of another quantity Normally differentiate all quantities with respect to time Example 2 on p 266 A Make a diagram I Y 10 The ladder is always 10 ft long dy 392 dt x The change in x is positive dx E 1 ftsec because x is increasing B Label diagram variables rates of change derivatives numerical values which do not change C Write an equation which relates all the variables x2 y2 102 dx dx dy dy 7 7 D Differentiate implicitly With respect to time 2x dt 2ya 7 0 2 xa ya 7 0 E Evaluate when When x 6 we can used the Pythagorean Theorem to get y 8 dx dy 7 dy 7 dy 7 7E F x y 7026183702dt7 4 G Answer questions completely include units and when The top of the ladder is sliding down because rate of change of y is negative the wall at a rate of 2 ft per second when the foot of the ladder is 6 ft from the wall and the foot is sliding away from the wall at a rate of 1 ftsecond Exercise 8 on p 269 A Diagram B Label 15 d x y dx x 4 y 4 dt 5 ftsec dt 15 x y 2 C Equation Based on similartriangles F 2 6x 6y 15y 2 y 5x d 7d 27d575dx D Differentiate implicitly With respect to time ax y 7 m x 5x 7 a x 7 53 E Evaluate when When x 40 this is actually irrelevant because there is no x in our differentiated equation 5dx75 R ER 55 G Answer The tip of his shadow is always moving at a rate of 8 ft per second whenever the man is walking away from the light pole at a rate of 5 ft per second
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