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tutorial 3sol - MATH 1007 TUTORIAL 3 1 Find the following...

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MATH 1007- TUTORIAL 3 1. Find the following limits, if they exist. i) lim lim ( ) ( )( ) lim x x x x x x x x x x x + = + = + = + = 1 2 2 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 0 ii) lim lim ( ) ( )( ) lim x x x x x x x x x x x → − + = → − + = → − + 1 2 2 1 2 1 1 1 2 1 1 1 1 1 DNE since lim x x x → − + = − ∞ + 1 1 1 and lim x x x → − + = ∞ 1 1 1 . iii) lim x x x x + 1 2 2 1 2 1 = + = = lim x x x x 1 2 2 1 2 1 0 0 iv) lim ( ) lim ( ) lim ( ) x x x x x x x x x x x x x x x + = + = + 3 1 1 3 3 2 3 3 3 3 3 2 3 3 3 3 3 2 3 3 = + = + = − + lim ( ) ( ) lim ( ) ( ) ( ) lim ( ) x x x x x x x x x x x x x x x x 3 3 3 3 2 3 3 3 3 1 3 3 3 3 3 1 3 3 3 = − + = − 1 33 3 3 33 1 9 . ( ) . v) lim lim . lim ( ) lim t t t t t t t t t t t t t t + = + + + + + = + + + = + + = 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 2 vi) lim lim lim . x x x x x x x x x x x x x + = + + = + + + + + + 0 1 9 1 3 1 0 3 9 3 9 0 3 9 3 9 3 9 3 9 = + + + + = + + + = + = − lim ( ) ( ) lim ( ) . ( ) x x x x x x
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