lim x->0 sinx/x
1
To find the limit of the function as x approaches zero, we can take the following steps:
1. First, substitute 0 for x in the function:
lim x->0 sinx/x = sin(0)/0
2. We can simplify the expression sin(0)/0 by using the fact that sin(0) = 0 and 0/0 is an indeterminate form. To resolve this indeterminate form, we can use L’Hopital’s Rule:
lim x->0 sinx/x = lim x->0 cosx/1 = cos(0)/1 = 1
3. Therefore, the limit of the function as x approaches zero is equal to 1. This can be seen visually by plotting the function, which approaches 1 as x approaches zero, as shown below:
Therefore, the final answer is:
lim x->0 sinx/x = 1
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