(1-cosx)/x (lim x -> 0)
To simplify this expression, we can start by using the identity:
lim x->0 (1 – cosx)/x = lim x->0 (1 – cosx)/(x-0)
Now, we can use the limit definition to evaluate this expression:
lim x->0 (1 – cosx)/(x-0) = lim x->0 (1 – cosx)/x
Since we have a 0/0 indeterminate form, we can use L’Hopital’s rule to further simplify the expression:
lim x->0 (1 – cosx)/x = lim x->0 (-sinx)/1
Now, we can evaluate the limit:
lim x->0 (-sinx)/1 = -sin(0)/1 = 0/1 = 0
Therefore, the limit of (1 – cosx)/x as x approaches 0 is 0
To simplify this expression, we can start by using the identity:
lim x->0 (1 – cosx)/x = lim x->0 (1 – cosx)/(x-0)
Now, we can use the limit definition to evaluate this expression:
lim x->0 (1 – cosx)/(x-0) = lim x->0 (1 – cosx)/x
Since we have a 0/0 indeterminate form, we can use L’Hopital’s rule to further simplify the expression:
lim x->0 (1 – cosx)/x = lim x->0 (-sinx)/1
Now, we can evaluate the limit:
lim x->0 (-sinx)/1 = -sin(0)/1 = 0/1 = 0
Therefore, the limit of (1 – cosx)/x as x approaches 0 is 0.
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