Evaluate the limit Lim Tan(x)/Sec(x)x→0
To evaluate the limit of (tan(x)/sec(x)) as x approaches 0, we can use the fact that tan(x) is equal to sin(x)/cos(x) and sec(x) is equal to 1/cos(x)
To evaluate the limit of (tan(x)/sec(x)) as x approaches 0, we can use the fact that tan(x) is equal to sin(x)/cos(x) and sec(x) is equal to 1/cos(x).
So, the given expression becomes:
lim (tan(x)/sec(x)) as x→0
= lim [(sin(x)/cos(x))/(1/cos(x))] as x→0
Now, we can simplify the expression by canceling out the common factor of cos(x):
= lim [sin(x)] as x→0
Since the limit of sin(x) as x approaches 0 is equal to 0, we can conclude that:
lim (tan(x)/sec(x)) as x→0 = 0
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