Evaluate the limit Lim Tan(x)/Sec(x)x→0
To evaluate the limit, we can use algebraic manipulation and trigonometric identities
To evaluate the limit, we can use algebraic manipulation and trigonometric identities.
First, let’s rewrite the expression as:
lim (tan(x)/sec(x)) as x approaches 0.
Since tan(x) = sin(x)/cos(x) and sec(x) = 1/cos(x), we can rewrite the expression as:
lim (sin(x)/cos(x)) / (1/cos(x)).
Now, we can simplify further by multiplying the numerator and denominator by cos(x):
lim (sin(x) * cos(x)) / (cos(x) * 1).
This simplifies to:
lim sin(x).
Finally, we evaluate the limit by plugging in the value of x as it approaches 0:
lim sin(x) = sin(0) = 0.
Therefore, the limit of tan(x)/sec(x) as x approaches 0 is 0.
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