Theorem 10:
If f and g are real functions such that fog is defined, if g is continuous at a point c, and if f is continuous at g(c), then fog is continuous at ..
Step I:
Factor of f(x) and g(x..
Proof:
Consider a circle with centre O and radius r. Join AB. Let the tangent at B meet OA produced at P. Draw BN perpendicular to OA. From ONB, BN = r sin q From OBP, BP = r tan q From the figure, we have Area of triangle OAB < Area of sector OAB < Area of triangle OBP ..
Consider a circle with centre O and radius r. Join AB. Let the tangent at B meet OA produced at P. Draw BN perpendicular to OA. From ONB, BN = r sin q From OBP, BP = r tan q From the figure, we have Area of triangle OAB < Area of sector OAB < Area of triangle OBP ..Proof:
We know that, Further, we have Substituting this value in (2), we have From (1) and (3), we have ..
We know that, Further, we have Substituting this value in (2), we have From (1) and (3), we have ..Proof:
..
..Infinite limits
Let f(x) be a function of x, if the value of f(x) can be made greater than any pre-assigned number by taking x close to 'a', then we say Similarly, if the value of f (x) can be made less than any pre-assigned number by taking x close to 'a', then we say f (x) tends to - as x approaches 'a'..
Let f(x) be a function of x, if the value of f(x) can be made greater than any pre-assigned number by taking x close to 'a', then we say Similarly, if the value of f (x) can be made less than any pre-assigned number by taking x close to 'a', then we say f (x) tends to - as x approaches 'a'..Suggested answer:
RHL = = 2 = ..
RHL = = 2 = ..Note:
We say that limit of f(x) exists at x = a, if l 1 and l 2 are both finite and equa..
See what our Users say :
This tutor was excellent. very clear on all of the problems. I would like to have more tutoring from Tutor Vista
Tutor helped me on every question and help me when i was confused. Thank you Tutor Vista
This Tutor Vista is GREAT! loved this session, it helped me heaps.
You are an amazing tutor. So knowlegeable and patient. Very clear in explanations, 2 thumbs up -kelly
Looking for More Help!
