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Does limit always tend to zero only?
No, limit can tend to any finite number including 0. It is also possible that the limit does not tend to any finite value or approaches infinity. Example: The limit of x^2+5 tend to 6 as x approaches -1.
What is limit of 1 cos x divided by x as x approaches 0?
Undefined: You cannot divide by zero
What is the lim as x approaches 0 of 3 times 1 - cosx divided by x?
First, you can take the constant factor 3 out, to obtain 3 times the limit of (1 - cos x) / x. Since this is of the form 0/0, you can use L'Hôpital's rule, which states that in such cases, you can take the derivative of both numerator and denominator. This results in the limit (as x approaches 0) of sin x / x, that is, 1 / 1 = 1. So, the final result is 3 times the limit of 1 = 3.
What is the integral of 2 times 1-x dx with limits 0 to t?
,/` 2(1 - x) dx,/` 2 - 2x dx2x - x2 ...evaluated from 0 to t gives us...2t - t2 - [2(0) - (0)2]2t - t2
What is the value of 1- cos x when x is small?
1 - cos x as x approaches 0. what is the cos of 0? It is 1. So as x approaches 0 cos x approaches 1. 1 - 1 = 0 So as it gets very small the solutions gets smaller.
