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Calculus Questions - All Grades

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College Integrals
Find the following indefinite integral:
∫(-7x2+4x-5x4)dx
  1. -7x3+4ln(|x|)-5x-3+C
  2. 13x3+4ln(|x|)+53x-3+C
  3. -73x3+4ln(|x|)+53x-3+C
  4. -14x-4x-2+20x-5+C
Grade 12 Derivatives
What is the derivative of f(x)=sin(3x2)?
  1. f′(x)=3x2cos(3x2)
  2. f′(x)=6xcos(3x2)
  3. f′(x)=3x2sin(3x2)
  4. f′(x)=6xsin(3x2)
Grade 12 Derivatives
What is the second derivative of f(x)=3x3+2x2?
  1. f′′(x)=18x+4
  2. f′′(x)=9x2+4x
  3. f′′(x)=18
  4. f′′(x)=0
Grade 12 Limits
Is h(x)=x-4x2-5x+4 continuous or discontinuous at x = 3? Justify using continuity test. If discontinuous, what type?
  1. Continuous
  2. Infinite discontinuity
  3. Jump discontinuity
  4. Removable discontinuity
Grade 12 Derivatives
Find the derivative. f(x)=5x2−6x+4
  1. f′(x)=10x-6
  2. f′(x)=5x-6
  3. f′(x)=25x
  4. f′(x)=7x-5
Grade 12 Limits
What is the limit of f(x)=3x3+2x2 as x approaches 5?
  1. limx→5f(x)=425
  2. limx→5f(x)=452
  3. limx→5f(x)=542
  4. limx→5f(x)=245
Grade 12 Derivatives
Identify the intervals on which the given function is increasing and decreasing.
f(x)=x3+x2-x
  1. Increasing: (-∞,-1)∪(13,∞); decreasing: (-1,13)
  2. Increasing: (-∞,-1); decreasing: (-1,13)
  3. Increasing for all x
  4. Increasing: (-1,13); decreasing: (-∞,-1)∪(13,∞)
Grade 12 Integrals
Find the value of ∫ln203e4xdx.
  1. 414
  2. 454
  3. 434
  4. 212
College Integrals
∫(8x8-6)dx
  1. 89x9+C
  2. 64x7+c
  3. 89x9-6x+C
  4. 89x9-6+C
Grade 12 Derivatives
On f(x)=2x5+x3-3x
  1. (-0.65,1.4) is a relative and absolute maximum.
  2. (0.65,-1.4) is a relative and absolute minimum.
  3. (-0.65,1.4) is a relative maximum.
  4. (0.65,-1.4) is a relative minimum.
  5. Both A and B.
  6. Both C and D.
  7. None of the above.
Grade 12 Derivatives
What is the derivative of f(x)=3x3+2x2?
  1. f′(x)=9x2+4x
  2. f′(x)=3x2+2x
  3. f′(x)=0
  4. f′(x)=12x2+6x
Grade 12 Derivatives
Find the derivative. f(x)=2x0.4-8x-0.02
  1. f′(x)=2x-0.4-8x-1.02
  2. f′(x)=0.8x-0.6+0.16x-1.02
  3. f′(x)=2+0.16x-1.02
  4. f′(x)=0.5x-0.6+0.4x-1.02
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