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lim n tends to infintiy ( {x} + {2x} + {3x}..... +{nx}/ n2(to the square) )where {X} denotes the fractional part of x?Ans) all no.s are positive or 0. so limit is either positive or 0.........(1)now {x}<=1;{2x}<=1;......{x}+{2x}+....{nx}<=nthat implies lim n tends to infinity{x}+{2x}+....{nx}/n^2 <= lmit n tends to infinity n/n^2;that means lim n tends to infinity{x}+{2x}+....{nx}/n^2 <= lmit n tends to infinity 1/n i.e. 0........(2)from (1) and (2);required limit=0;
1/cos(x-a)cos(x-b)
Parallel Vectors - Applications of Scalar Multiplication This is an idea that we will see fairly a bit over the next couple of sections. Two vectors are parallel if they have
Evaluate both of the following limits. Solution : Firstly, the only difference among these two is that one is going to +ve infinity and the other is going to negative inf
a. Write an exponential function that could model the information in this graph. b. Describe a business, scientific (not mathematical), or economic situation for what thi
Another aid that can help children practise subtraction is the number strip. TGS can be used to improve their ability to count backwards. For example, subtracting 4 from 9 means
Find out all the numbers c that satisfy the conclusions of the Mean Value Theorem for the given function. f ( x ) = x 3 + 2 x 2 -
a car comes to a stop from a speed of 30m/s in a distance of 804m. The driver brakes so as to produce a decelration of 1/2m per sec sqaured to begin withand then brakes harder to p
BROKARAGE.
how to break fractions
Q. Probability of Independent Events? Ans. Consider these two events: {My name is Shirley} {The rain is falling} Are these events related to each other? No. My name
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