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What is limit of 1 -cos x divided by x as x approaches 0?
1
What is the exact trigonometric function value of cot 0?
There is no value cot 0, because cot 0 is equivalent to 1 / tan 0, which is equivalent to 1 / 0, which is undefined. That said, the limit of cot x as x approaches 0 is infinity.
What does a number over infinity equal?
0. This is the same as the limit of 1/x as x approaches infinity, which is is 0. This is because 1/1,000 = .001 and 1/1,000,000 = .000001 and 1/100,000,000,000 = .0000000001 etc.
What is the 2 divided by infinity?
It is 0. Think of dividing 2 by a very big number. For example, 2/20000000000= 1/10000000000 which is very close to 0. As the denominator gets bigger and bigger, the quotient approaches 0. In the limit it is 0. Remember infinity is not really a number. In this case it means, letting the denominator get as big as it can. Another way to think of or write this this is lim n-->0 of 2/n=0
How do I evaluate the limit sin9x divided by tan9x when x tends to 0 without using L Hospitals rule?
First to simplify matters, change y=9x. So we are looking at limit sin(y) divided by tan(y).Now lets look at right angled triangle wheresin(y) = a/ctan(y) = a/bthus we are looking at the limit of (a/c)/(a/b) = limit of b/cAs the angle y shrinks, the right angle remains constant, and the remaining angle approaches a right angle. Thus at the limit we have a triangle with equal angles and thus where b=c.As a result limit you are trying to calculate is 1.
