Conclusion
In this chapter, we have studied various types of functions and their graphs. The use of graphs also facilitate the study of domain and range of functions...
Limits (Contd....)
Limits of Trigonometric Functions and Sandwich Theorem: for all x in some open interval containing c and suppose ..
Limits of Trigonometric Functions and Sandwich Theorem: for all x in some open interval containing c and suppose ..Theorem 4 (Sandwich Theorem): for all x in some open interval containing c and suppose Since f is sandwiched between two functions g and h, the above theorem is known as sandwich theore..
for all x in some open interval containing c and suppose Since f is sandwiched between two functions g and h, the above theorem is known as sandwich theore..Note 2:
=..
=..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'..One Sided Limit
We have discussed earlier about right hand limit and left hand limit. Both these limits are called one sided limits. x approaches a from the right side and through values greater than a. For a function f(x), we say as left hand Limit, as x approaches a from the left and through the values less..
We have discussed earlier about right hand limit and left hand limit. Both these limits are called one sided limits. x approaches a from the right side and through values greater than a. For a function f(x), we say as left hand Limit, as x approaches a from the left and through the values less..See what our Users say :
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