खुदरा आपूर्ति श्रृंखला प्रबंधन को परिभाषित कीजिए। इसके प्राथमिक उद्देश्यों की व्याख्या करें और यह पारंपरिक थोक आपूर्ति श्रृंखला प्रबंधन से किस प्रकार भिन्न है?

Verify the second mean value theorem for the function  and  in the interval .

  Show that the function  defined by  has an inverse by applying the inverse function theorem. Find its inverse also.

   Apply Bonnet Mean Value Theorem for integrals to show that

  Use the Fundamental Theorem of Integral Calculus to evaluate the integral

 Using Weiestrass M-test, show that the following series converges uniformly.

Check whether the set of integers is countable or not.

  Show that the equation  has a real root other than 

 Using the principle of mathematical induction, show that

 Show that  is an algebraic number.

 Find a and b such that  exists.

   Use Cauchy's mean value theorem to prove that:

 a)      If the partition P₂ is a refinement of the partition P₁ of [a,b], then  and . Verify this result for the function  defined over the interval  and the partitions  and .
        b)      Evaluate: .

Show that , the lagrange's form of remainder in the Maclaurin series expansion of e^4x, tends to zero as . Hence obtain the Maclaurin's infinite expansion for e^4x.

 Determine the local minimum and local maximum values of the function f defined by .

a)      Test the following series for convergence,

  (i)    
                (ii)   
        b)      Show that  is conditionally convergent.

Verify Bozano-Weierstrass Theorem for the following sets:
i)      Set of non-negative integers.
ii)     Interval 
d)      Check whether the limit  exists or not?

Write the inequality  in the modulus form.

  Prove that a strictly decreasing function is always one-one.

Check whether the intervals ]5,9] and [6,12[ are equivalent or not.