ECAT (Pre-Eng) Mathematics Chapter 18 Basic Concepts & Definitions

If x = at² and y = 2at then dy/dx =

• 2a/y A
• y/2a B
• -a/2y C
• -2y/a D

d/dx (cosec x)

• -sec x tan x A
• sin x cos x B
• -csc x cot x C
• 2sin x cos x D

If y = 1/x² then dy/dx equals:

• -2x A
• x^-3 B
• -2/x³ C
• -2x³ D

• 0 A
• 8 B
• 5 C
• 9 D

If∱(x) = 2x³ + 1 then∱¹(0) =

• 0 A
• 1 B
• 6 C
• None of these D

If 3x + 4y +7 = 0 , then dy / dx =

• -1/2
  A
• -4/3 B
• 7/2 C
• -3/4 D

• 
  A
• 
  B
• 
  C
• 
  D

If y=x^mthen dy/dx equals:

• mx A
• x/m B
• mx^m-1 C
• xm^m-1 D

∱(x) = ax²-3x -5, and∱¹ (2) = 9, a is equal to

• 2 A
• 3 B
• -2 C
• 4 D

Let∫ be real valued function continuous in the interval (x,x₁)⊆ D∫ (the domain of∫),

then∱(x₁) -∱ (x)/x₁-x represents:

• Instantaneous rate A
• Average rate of change B
• Differential coefficient C
• None of these D

If f(x) = c then∱¹(x) equals:

• 1 A
• 0 B
• cx C
• c D

• zero at x A
• differentiable at x B
• continuous at x C
• none of these D

If c is a constant, then d/dx (c) =

• 0 A
• c B
• cx C
• 1 D

• -2x A
• x^-3 B
• 
  C
• -2x³ D

If ∱(x) = x^2/3then∱¹(x) at x = 8 equals:

• 8 A
• 1/8 B
• 1/3 C
• 2/3 D

if x∈ D∱ and∱^{1(x) exists, then}∱ is said to be

• zero at x A
• Differentiable at x B
• Continuous at x C
• None of these D

The derivative of 1/x^m is:

• x^m+1/ m A
• m(x)^m-1 B
• (m-1) x^-m C
• m/x^m+1 D

• 
  A
• x^n-1 B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

d / dx (cot x) =

• Sec x tan x A
• -csc² x B
• Sec² x C
• 1/cot² x D

If∱(x) = x⁵ + x³ + x the value of∱¹(1) is:

• 0 A
• 8 B
• 5 C
• 9 D

If∱(x) = x^-100the value of∱¹ (1) is:

• 100 A
• -100 B
• 0 C
• -101 D

• 
  A
• 
  B
• 
  C
• 
  D

• x²+ 2 A
• 3x + 2 B
• 3x²+ 5 C
• 3x²+ 2 D

d/dx (cos x sin x) =

• cos² x - sin² x A
• 2cos² x + sin² x B
• 2cos² x - sin² x C
• 1 - sin² x D

• 
  A
• 
  B
• 
  C
• 
  D

If y = xⁿthen dy/dx equals:

• nx A
• x^n-1 B
• nx^n-1 C
• n D

• mx A
• x/m B
• mx^m-1 C
• xm^m-1 D

• 
  A
• 
  B
• 
  C
• 
  D