Problems for Labs
1.Find the slope of the line tangent to the curve x y e 2 x−y 2 at the point 1,1
on the curve.
2.Find an equation of the line tangent to the curve y x − 1 2x − 3 5 − 2x at the
4x − 7 13 − 6x 5
point 2,1on the curve.
3.A hard boiled egg is removed from a pot of hot water at 101 C and is left to cool
in a room where the temperature is maintained at 20 C. After 10 minutes the egg has
cooled to a temperature of 74 C. 0
a What is the temperature of the egg after 20 minutes?
b When will the egg’s temperature be 36 C? 0
Assume Newton’s Law of Cooling.
4.A cup of boiling water 100 C is placed outside. One minute later the temperature of
the water is 70 C and after another minute, its temperature is 49 C.What is the outside
temperature (the medium)?
5.The half life of a radioactive substance is about 300 years. In how many years will
only one − fourth of the original amount remain?
6.Find the half life of a radioactive substance if after 60 days, 75% of the original
amount has disintegrated.
7.Find the exact values of
i cos1 1 ii sin −1 iii csc −2
8.True or False :
a tantan 100 100 b tan tan100 100
9.Find exact values of
a tantan 100 b cossec 2