Math Problem Solver

9(a)If (1, 3) is an extremity of a diameter of the circle 3x

2

+ 3y

2

+ 6x – 12y – 2 = 0, then find

the other end point of the diameter.

OR

9(b)If 𝑦 = 𝑥

𝑥

,then find 𝑑𝑦

𝑑𝑥

.

10(a)Evaluate: 𝑙𝑖𝑚𝑥→0

1−cos 𝑥

𝑥

2

.

OR

10 (b)Find the equation of tangent to the curve 𝑦

2 = 8𝑥, at (2, 4).

11(a) Find 𝑑𝑦

𝑑𝑥

, if 𝑥 = 𝜆𝑡 and 𝑦 =

𝜆

𝑡

.

OR

11(b)If 𝑢 = 𝑡𝑎𝑛

−1

𝑦

𝑥

, then prove that 𝜕

2𝑢

𝜕𝑥

2 +

𝜕

2𝑢

𝜕𝑦

2 = 0.

12(a)The sum of two numbers is 20. Find the numbers such that the sum of their

squares is minimum.

OR

12 (b)Find the angle between the curves𝑦 = 𝑥

2

and𝑥

2 = 𝑦.