+584 Assume f(x)is nonnegative in an open interval containing c and \(\lim_{x\rightarrow c}f(x)=0\)
(a) if\(\lim_{x\rightarrow c}g(x)=infinity\),show that \(\lim_{x\rightarrow c}{f(x)}^{g(x)}=0\)
(b)if \(\lim_{x\rightarrow c}g(x)=-infinity\),show that \(\lim_{x\rightarrow c}{f(x)}^{g(x)}=infinity\)
By the way,How do you type infinity as a math symbol in here?Thank you!
+1904 ∞. On my MacBook Pro I hold down the option key and then push the 5 key. On a PC, hold down the ALT key and then push the 2 key, then the 3 key, and then the 6 key all on the num-lock keypad.
+1904 ∞. On my MacBook Pro I hold down the option key and then push the 5 key. On a PC, hold down the ALT key and then push the 2 key, then the 3 key, and then the 6 key all on the num-lock keypad.
+33661 As x → c f(x) gets smaller than 1 at some point and g(x) gets larger than 1 at some point.
(a) A number smaller than 1 raised to a power larger than 1 is even smaller then the small number, so the combination tends to zero.
(b) With g(x) tending to -infinity, you have the combination tending to 1/0 (i.e. tending to infinity).
