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Say True or False with proof
Q1. If π(π₯) = 2|π₯ β 1| and π(π₯) = 3π₯ β 10,
then πππ(1) = 12.
Q2. (β2, 1,1/2)β πΈ Γ π Γ πΉ.
Q3. The domain of the function f defined by π(π₯)
=β{(3-x)/(x-2)} is R-{2}.
Represent the rational functioο»Ώn f(x)=1/3x-1 using its table values and graphx=R^n
x=(x1,x2,x3,x4,....,xn).
y=(y1,y2,y3,y4,....,yn)
d(x,y)=β((x1-y1)^2+(x2-y2)^2+(x3-y3)^2+......+(xn-yn)^2)
Show that d is metric on x
For an example of a discontinuous linear functional on a normed linear space
prove ||Ax|| < ||A|| ||x||
Example of metric space but not norm
Let (X,d) be a metric space and consider the subset A β X and B β X . Show that the closure satisfies the following property closure( A βͺ B) =closure(A) βͺ closure(B)
Show that a norm on a vector space X is a sublinear functional on X
If a function f is not defined at x = a then the limit lim f(x) as x approaches a never exists. true or false
Let x1 x2 β¦ . . xn, be an orthonormal set in X and π1 ,π2,. β¦ β¦ β¦Β
πnbe scalars
having absolute value 1. Then π1x1 + π 2x 2+ β― β¦ π nxn= x1 + β― +Β
xn
#340153 on Dec 2023