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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;
Example: find out the slope of equations and sketch the graph of the line. 2 y - 6x = -2 Solution To get the slope we'll first put this in slope
Before going to solving differential equations we must see one more function. Without Laplace transforms this would be much more hard to solve differential equations which involve
If secA= x+1/4x, prove that secA+tanA=2x or 1/2x. Ans: Sec? = x + 1/4x ⇒ Sec 2 ? =( x + 1/4x) 2 (Sec 2 ?= 1 + Tan 2 ?) Tan 2 ? = ( x +
find dy/dx of cosx
Limit Comparison Test Assume that we have two series ∑a n and ∑b n with a n , b n ≥ 0 for all n. Determine, If c is positive (i.e. c > 0 ) and is finite (i.e. c
The distribution of sample means is not always a normal distribution. Under what circumstances is the distribution of sample means not normal?
If 3/5=5,4/7=8,8/7=6 then, what should 9/6 be ?
Raul's bedroom is 4 yards long. How many inches long is the bedroom? There are 36 inches within a yard; 4 × 36 = 144 inches. There are 144 inches in 4 yards.
how it will be ? = ? + Ø
If A, B are acute angles and sinA= cosB, then find the value of A+B. Ans: A + B = 90 o
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