Lt.(tanx)^tan2xx->45

first let x approach 45 from below: tanx <1 and tan2x→+∞,therefore left hand side limit is zero.

x approaches 45 from above: tanx >1 and tan2x→ -∞, therefore right hand side limit is zero

Therefore the answer is that the limit is zero.

Approved

this is not the answer.

lt. (tanx)^tan2x x->45 = e^lt. (tan2x)(tanx-1) x->45 now calculate the limit of lt. (tan2x)(tanx-1) x->45 it is equals to (-1) ans. is e^-1=1/e

Approved