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1. If the function f is monotonic on (a,) then ’f’ is ______________ on (a,b) 2. Riemann Integral S(P,f)=____________ 3.

19 / 01 / 2019 Maths

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. If Vf (a,b) ↔ f is   a) Bounded     b)Continuous   c)Increasing   d)None  2. The Point (x,y)  obtained by solving fx=0 and fy=0 as known as  a) Saddle Point  b)Extreme Point  c)Critical Point    d)None  3. A function which is increasing and  decreasing is known as  a) Bounded   b) Continuous     c) Analytic   d)Monotonic   4. A function f is said to be a function of Bounded variation then                 a) ∑|∆fk|≥M   b) ∑|∆2fk|0 then q is called                 a) Positive definite  b) Negative definite   c) Semi positive   d) Semi Negative          9.   If Q= Y|DY is known as                a) Signature of Q   b)Index of Q   c) Diagonal of Q   d) None        10.  In computation of M‐P Inverse A|A=               a)B      b)A      c)I       b) A|        Fill in  the Blanks:  (10*1/2=5) 
1. If the function f is monotonic on (a,) then  ’f’ is ______________ on (a,b)  2. Riemann Integral S(P,f)=____________  3. Total Variation Vf (a,b) = ____________  4. ∆ fk =  5. The Taylor’s expansion of f(a+h,b+k)=___________________________  6. The rank of moore Penrose inverse of A =____________  7. If H is idempotent then H2  8. If A is Positive definite then the characteristic roots of A are _________  9. In the Gram Schmidt orthogonalization process the basis Zk=___________  10. The Moore Penrose inverse is always _______________   
Answer the following (10*1=10) 
1. Define Extreme and saddle point  2. Define Simultaneous limit  3. Define Repeated limit  4. Define Riemann stielties  integral(RS Integral)  5. What is finer partition  and give one example  6. Define Quadratic form and index and signature  7. Define orthogonal basis and orthonormal basis   8. Gram Schmidt Orthogonalization process  9. Prove if AX=g is consistent iff AA‐|g=g  10. Define GramMatrix 

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