2nd Year Mathematics Chapter 2 TestUNIT 2: FURTHER DIFFERENTIATION

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

1. When finding the global extrema of a function on a closed interval [a,b], at which points should you first evaluate the function?

   1. Only at the point x=0

   2. Only at the midpoint of the interval

   3. At all critical points and endpoints of the interval

   4. At infinity

2. Find for the parametric equations x=sin² t and y= cos 2t:

   1. =-2

   2. =2

   3. = - tan t

   4. =- 4sint cot t

3. Differentiation will be applied to identify which behavior of functions?

   1. ncreasing and decreasing functions

   2. Domain and range

   3. Periodic behavior

   4. Continuity and limits

4. What is the approximate value of the mathematical constant e used in the natural exponential function?

   1. 3.14159

   2. 2.71828

   3. 1.41421

   4. 1.61803

5. The approximation provided by the tangent line is highly accurate for:

   1. All real numbers infinitely

   2. Large values of x far from the point

   3. A small interval on either side of the point of tangency

   4. Negative values of x only

6. Simplify and find the derivative  of the function :

   1. = 2 tan x

   2. = 2 cot x

   3. = -2cot x

   4. = -3 cotx

7. If a^y =x, then what is the correct logarithmic representation?

   1. y=log_a x

   2. x=log_a y

   3. y=log_x a

   4. a=log_y x

8. Use the differential (dy) to approximate the change  for  when x changes from 3 to 3.02.

   1. 0.26

   2. 0.52

   3. 0.02

   4. 26.0

9. What condition must be met to continue finding successive derivatives of a function?

   1. The function must equal zero

   2. The function must be linear

   3. The new function must remain differentiable

   4. The function must be explicit

10. The side of a cube is measured to be 30 cm with a maximum error of 0.14 cm. Find the maximum error in the calculated volume of the cube.

    1. 126 cm³

    2. 378 cm³

    3. 2700 cm³

    4. 12.6 cm³