- #1
bard
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lim(x->pi/4) tan(2x) =tan(pi/2) wat to do after this, it is undefined
To solve this limit, we can use the trigonometric identity tan(2x) = 2tan(x)/(1-tan^2(x)). Substituting x=pi/4, we get 2tan(pi/4)/(1-tan^2(pi/4)). Using the fact that tan(pi/4)=1, we get 2/(1-1)=2/0. Since the denominator is approaching 0, we can use L'Hopital's rule to get the limit as 2. Therefore, lim(x->pi/4) tan(2x) = 2.
No, the Squeeze Theorem can only be used for finding limits as x approaches a specific value, not as it approaches infinity or a multiple of pi.
When approaching from the left, the value of the limit is 2. However, when approaching from the right, the value of the limit does not exist as the function tan(2x) oscillates between positive and negative infinity.
Yes, we can also use the trigonometric identity tan(2x) = sin(2x)/cos(2x). Substituting x=pi/4, we get sin(pi/2)/cos(pi/2) = 1/0. Again, using L'Hopital's rule, we get the limit as 2.
When a limit approaches a value that is undefined, it means that the function is approaching either positive or negative infinity, and does not have a finite value at that point.