# Multivariable calculus all previous/ past question papers

Sessional 1 question paper

Sessional 2 question paper

Final question paper

## Multivariable calculus Final paper

**Q1:**

a) Define the following. Chain Rule.

b)Horizontal line test for One-to-One functions

Use L’Hospital’s Rule to find the limit sin.x-cosz

**Q2:**

16 sin’x cos³x dx

**Q 3:**

- a) Find area of the region enclosed by two curves, y=2-x² and the line

y = -x. b) Use logarithmic differentiation to find if 7 (5)

x>1 Q4: a) Evaluate by using suitable substitution.

y x-1

(1+ean) sec²0 de

y=t-t³.

- b) Find as a function of fif x=t-t² (5)

**Q5:** a) One model for the way diseases die out when properly treated assumes that the dy rate at which the number of infected people changes is proportional to number y. The number. of the people cured is proportional to the number that has disease. Suppose that in the course of any given year the number of cases of a disease is reduced by 20%. If there are 10000 cases today, how many years will it take to reduce the number to 1000? b) Evaluate by completing square.