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Evaluating Limits

Please find the limits and justify the answer:

a) lim 2^x - x² + pi
x→0 ‾‾‾‾‾‾‾‾‾‾‾‾
x^10

b) lim sin 2x
x→0 ‾‾‾x‾‾

c) lim (1 - 1/x)^x
x→∞

(^ means exponent)

Solution Preview

Please find the limits and justify the answer:

a) lim 2^x - x² + pi
x→0 ‾‾‾‾‾‾‾‾‾‾‾‾
x^10

Solution. As
lim 2^x - x² + pi=1+pi
x→0
and
lim x^10=0,
x→0
we conclude that

...

Solution Summary

Limits ae found.

$2.19