What is the limit as x approaches 0 of [(tanx)^2]/x?
what did you not understand about my previous response?
oops, Isee, it was tan squared.
hang on.
(tanx)^2 cannot be simplified to sinx/cosx because it's squared
lim tan^2/x= lim sinx/x * lim sin x * lim1/cosx * lim 1/cos x
There is a theorem that says lim xzy= lim x lim y lim z
so lim tan^2x/x= 1*0*1/1*1/1=0
Thank you!
To find the limit as x approaches 0 of [(tanx)^2]/x, we can use algebraic manipulation and a known limit.
Step 1: Rewrite the expression
[(tanx)^2]/x can be rewritten as (tanx/x)^2.
Step 2: Recognize a known limit
The limit as x approaches 0 of tanx/x is a known limit and is equal to 1.
Step 3: Apply the known limit
Taking the square of a known limit means squaring the result, so we have (1)^2 = 1.
Therefore, the limit as x approaches 0 of [(tanx)^2]/x is equal to 1.
In summary:
[(tanx)^2]/x = (tanx/x)^2 = (1)^2 = 1.