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Calc 1 Lab 6 pg2 - You can check if the tangent line is...

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Unformatted text preview: You can check if the tangent line is correct by plotting the function and the tangent line on the same graph. The Problems For each of the following functions find x h — . x h — f( + i for) and hmfl + ) f(x) haO h Then for the given x find the slope and the equation of the tangent line. Finally, graph the function and the tangent line on the same axis to show that the slope and equation are correct. 3' _ 3 _ 5/0 a: 2, A =mx4io S/Ofczzz 'x i/ A f(x)—x,x—2 f 2X J2 )/{/zx+é foin+:(z,g) B. fix)=x4, x=-2 f/vf’e=’27— 2 want 8=21fé C. f(x)=x5,x:-l S/ofg: 512:5” —/{;b Do you see the pattern??? l i \JZXZV D. f(x)=2x2—5x+6, x=2 l 4)“ E. f(x)=(3x—l)/(2x+5),x=4 1 ‘ PART H EVALUATING SOME LIMITS Limits show up in many different applications in calculus. Generically, we can talk about limF(x) = L I46 The limit of F (x) as x approaches c is L. Here c and L are numbers. (Note that there is nothing sacred of using h for the variable in limit problems. Informally we say that the value of F(x) approaches L as x approaches c. Just like in some of the Difference Quotient problems we can ofien ( but not always ) use algebra to simplify the expression and then easily see what the limit is. For instance, 2 Z _ 11m" 1=lim(x+l)=2 or limM=hm(2x+S)=7. x—>l x._.1 1—)] x91 x_1 x—>I V ...
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