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The Mean Value Theorem : In this section we will discuss the Mean Value Theorem.
Before we going through the Mean Value Theorem we have to cover the following theorem.
Rolle's Theorem : Assume f ( x ) is a function which satisfies all of the following.
1. f ( x ) is continuous on the closed interval [a,b].
2. f ( x ) is differentiable on the open interval (a,b).
3. f ( a ) =f (b )
Then there is a number c such that a < c < b and f ′ (c ) = 0 . Or, in other terms f ( x ) contain a critical point in (a,b).
t=w,w 2 L.H.S (w+w 2 ) + (w 2 + w) 2 ........ 1 + 1 ..... But every third term is of the form: (w 3n +w 3n ) 2 =22 There are nine such terms. Their sum is 36. The rema
Class limits These are numerical values, which limits uq extended of a given class that is all the observations in a provided class are expected to fall in the interval which
1. If the equation has any fractions employ the least common denominator to apparent the fractions. We will do this through multiplying both sides of the equation by the LCD. Al
Evaluate following limits. Solution Therefore we will taking a look at a couple of one-sided limits in addition to the normal limit here. In all three cases notice
if 1/x+2, 1/x+3, 1/x+5 are in AP find x Ans 1/x+2,1/x+3, 1/x+5 are in AP find x. 1/x+3 - 1/x+2 = 1/x+5-1/x+3 => 1/x 2 +5x+6 = 2/ x 2 +8x +15 => On solving we get x
three prices are to be distributed in a quiz contest.The value of the second prize is five sixths the value of the first prize and the value of the third prize is fourfifth that of
you have RM5O,OOO to invest,and two fund that you''d like to invest in.The You-Risk-It Fund yields 14% interest.The Extra-Dull Fund yields 6% interest.Besause of college financial-
Q. How to Subtract fractions involving negative numbers? Ans. This is the same as adding them, but just remember the rule that two negatives on the same fraction cancel ou
In how many ways 30 identical balls can be DISTRIBUTED among 4 boys?? Ans) Let they get a,b,c,d respectively. You requireto find the non negative integral results of a+b+c+d=3
Verify Liouville''s formula for y^ prime prime prime -y^ prime prime - y'' + y = 0 in [0, 1]
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