Calculus questions

1.For ?(?) = 2?2 + ? − 4 , ?(?) = 7 − ?2 compute each of the following:

  1. Evaluate the following limits:
  2. Differentiate the following :
  3. Derive the formula for the Product Rule for four functions.
  4. Evaluate each of the following integrals:
  5. Find the general solution of the differential equation given below:
  6. Solve the initial value problem:
  7. Describe the applications of the Integration with real life examples (150 words) .
  8. Write a detailed note on the applications of differential equations in real world problems.

Give at least two Examples.

Sample Solution