Precise Definition: We say lim f(x) = L if for every e > 0 there is...

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Precise Definition: We say lim f(x) = L if for every e > 0 there is a 8 >0 such that whenever 0 0 and x' is real for negative x b then lim-0 Note: sgn(a)=1 if a>0 and sgn(a)=-1 if a <0. 1. lime & lime=0 lim f(x)= lim f(x)=L⇒ lim f(x)=L 4. lim Basic Limit Evaluations at t f(x) g(x) 5. lim[/(x)] = [lim/(x)] 6. lim[√(x)=√lim f(x) 5. n even: lim x² = ∞ Visit http://tutorial.math.lamar.edu for a complete set of Calculus notes. provided lim g(x)0 6. n odd: lim x² = & lim x² = -0 7. n even: lim ax² ++bx+c=sgn(a) ∞ 8. n odd: lim ax ++bx+c=sgn(a) 9. nodd: lim ax ++cx+d=-sgn(a) Please show all the steps, it's easier for me to see how you jumped from one part to another. Thank you! Ⓒ2005 Paul Dawkins Integrate: (a) da (b) tan²z+1dr z Precise Definition: We say lim f(x) = L if for every e > 0 there is a 8 >0 such that whenever 0 0 and x' is real for negative x b then lim-0 Note: sgn(a)=1 if a>0 and sgn(a)=-1 if a <0. 1. lime & lime=0 lim f(x)= lim f(x)=L⇒ lim f(x)=L 4. lim Basic Limit Evaluations at t f(x) g(x) 5. lim[/(x)] = [lim/(x)] 6. lim[√(x)=√lim f(x) 5. n even: lim x² = ∞ Visit http://tutorial.math.lamar.edu for a complete set of Calculus notes. provided lim g(x)0 6. n odd: lim x² = & lim x² = -0 7. n even: lim ax² ++bx+c=sgn(a) ∞ 8. n odd: lim ax ++bx+c=sgn(a) 9. nodd: lim ax ++cx+d=-sgn(a) Please show all the steps, it's easier for me to see how you jumped from one part to another. Thank you! Ⓒ2005 Paul Dawkins Integrate: (a) da (b) tan²z+1dr z

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a To integrate the function x9 sqrt1 x20 with respect to x we can use the substitution method Lets s... View the full answer