The sides of an equilateral triangle are increasing at the rate of 2 cm/see, Find the rate at which its area increases, when side is 10 cm long.

2

(a)

If x changes from 4 to 4.01, then find the approximate change in log, x.

2

(a)

The side of an equilateral triangle is increasing at the rate of 5 cm/sec. At what rate its area increasing when the side of the triangle is 10 cm.

2

(a)

The length x of a rectangle in decreasing at the rate of 5 cm/min and the width y increasing at the rate of 4 cm/min. find the rate of change its area when x = 5 cm and y = 8 cm.

2

(a)

The volume of a cube increasing at the rate of 9 cm³/sec. How fast is the surface area increasing when the length of an edge is 10 cm.

2

(a)

Find the point on the curve \(y^2 =8x + 3\)  for which the y-coordinate changes 4 times more than coordinate of x.

2

(a)

Find the slope and tangent and normal to the curve \(x^2+2y+y^2=0\ at \ (-1,2).\)

2

(a)

Show that the tangents to the curve \(y=x^2-7x+18\) at (3, 0) and (4, 0) are at right angles.

2

(a)

Find the value of a if tangent to curve y = x²-ax + 7 is parallel to the line 2x - y + 9 = 0 at (- 1, 1).

2

(a)

Use differentials find the approximate value of \((127)^{1/3}\) .

2

(a)

Use differentials find the approximate value of \((0.037)^{1/2}\)

2

(a)

Find an angle \(\theta\) which increases twice as fast as its sine.

2

(a)