limit as x approaches 0: sinx/x
1
The limit as x approaches 0: sinx/x is one of the fundamental limits in calculus. Let’s see how to solve it:
We know that the standard value of sinx/x is 1, therefore, if we substitute x=0 in the expression sinx/x directly, we get an indeterminate form of 0/0.
In order to proceed, we need to use the L’Hôpital’s rule, which states that if we have an indeterminate form of 0/0 or ∞/∞, we can differentiate the numerator and denominator until we get a non-zero value.
Let’s apply L’Hôpital’s rule to the given limit,
lim x→0 sinx/x
= lim x→0 d/dx(sinx)/ d/dx(x) (by applying L’Hôpital’s rule)
= lim x→0 cosx/1
Now, we can substitute x=0 in the expression, and we get cos0/1 = 1.
Therefore, the limit as x approaches 0: sinx/x is equal to 1.
More Answers:
Master The Basics: A Guide To Calculus Derivative Rules For Effective Function DifferentiationAnd Applying The Continuity Rule In Calculus Functions.
Mastering Limits In Calculus: Evaluating (1 – Cos(X))/X As X Approaches 0
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