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**Continuity & Differentiability**

**Question 1:**

**Answer**

**Question 2:**

**Answer**

**Question 3:**

**Answer**

**Question 4:**

**Answer**

The given relationship is

Differentiating this relationship with respect to x, we obtain

**Question 5: **

**Find **

**Answer**

The given relationship is x^{2} +xy +y^{2} = 100

Differentiating this relationship with respect to x, we obtain

[Derivative of constant function is 0]

**Question 6:**

**Answer**

**Question 7:**

**Answer**

Using chain rule, we obtain

**Question 8:**

**Find **

**Answer**

The given relationship is

Differentiating this relationship with respect to x, we obtain

**Question 9:**

**Find **

**Answer**

Therefore, by quotient rule, we obtain

**Question 10:**

**Answer**

**Question 11:**

**Answer**

The given relationship is,

On comparing L.H.S. and R.H.S. of the above relationship, we obtain tany/2 = x

Differentiating this relationship with respect to x, we obtain

**Question 12:**

**Answer**

The given relationship is

From (1), (2), and (3), we obtain

Differentiating this relationship with respect to x, we obtain

**Question 13:**

**Answer**

**Question 14:**

**Find **

**Answer**

Differentiating this relationship with respect to x, we obtain

**Question 15:**

**Find dy/dx **

**Answer**

Differentiating this relationship with respect to x, we obtain

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