This paper circulates around the core theme of 1. If the function f is monotonic on (a,) then ’f’ is ______________ on (a,b) 2. Riemann Integral S(P,f)=____________ 3. together with its essential aspects. It has been reviewed and purchased by the majority of students thus, this paper is rated 4.8 out of 5 points by the students. In addition to this, the price of this paper commences from £ 72. To get this paper written from the scratch, order this assignment now. 100% confidential, 100% plagiarism-free.
. 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