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# Math sheet - e conditionally 0 m equation values ries...

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+b(n)n(n+1)=1nn+1 1, b=-1 = ∞( - + ) n 0 1n 1n 1 (11-12)+(12-13)+…+(1n-1n+1) 11-1n+1 where n 1 n=0 fn(0)n!xn n=0 en0n!xn ex for all n 1 n=0 xnn! he value of - e x2 urin for = = ∞ ! ex n 0 xnn - = = ∞(- ) ! e x2 n 0 x2 nn ane equation values to solve for t Plug in t to find values + - - + - + = 5 t 24 2t 3 2 3t 12 for point where the line meets x=6.5 y=1 z=2.5 (6.5,1,2.5) om parallel plane and containing a point e parallel to plane - + = x 2y 3z 12 and P(5,4,-2) plane H. h P, and the normal of the given plane is n of the new plane is (x-5)-2(y-4)+3(z+2)=0 2+x33+…+C= 0 xn+1n+1+C=1 xnn+C -… x33 eries is conditionally ent 2 2 =∞ nes L 1 and L 2 : r(t) = (3+t)i + (1-t)j + (5+2t)k d z values are equal you have one, plug in to find intersection point. he intersection is at (1,3,1) en by s and t. b3=abcos θ product values ning point P = z 12 and is <1,-2,3>, the equation for the line is - = - - = + x 51 y 4 2 z 23 Increasing: < + an an 1 for all values of n sufficiently large Decreasing: > + an an 1 for all values of n sufficiently large Monotone: Function is either increasing or decreasing.
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