- #1
chukie
- 80
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Solve:
lim x->0 (tan 3(x+h)-tan(3x))/h
i hv no clue where to start =(
lim x->0 (tan 3(x+h)-tan(3x))/h
i hv no clue where to start =(
Dick said:Did you mean lim h->0??
rootX said:It is actually very simple.. don't even need to any trig after simplifying tan(3x+3h) ..
should factor out things.. and they would cancel out nicely.
And, one more thing tan(x)/x = 1 .. (which is simple to prove is you know sin(x)/x =1 as x-->0)
The limit of the tangent function at h=0 is undefined or does not exist.
The tangent function is a periodic function with a period of π, meaning that at h=0, the value of the function jumps from -∞ to ∞. This causes the limit to not exist.
No, the limit of the tangent function at h=0 cannot be solved using algebraic methods. It can only be determined by graphing or using trigonometric identities.
The limit of the tangent function at h=0 is related to the concept of vertical asymptotes. As h approaches 0, the tangent function approaches vertical lines at x=π/2 and x=-π/2, which are the vertical asymptotes of this function.
Yes, the concept of limits and asymptotes, including the limit of the tangent function at h=0, is used in various fields of science and engineering, such as calculus, physics, and electrical engineering. It is also used in computer programming to create smooth curves and avoid errors in calculations.