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Calculus Questions - All Grades

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Grade 12 Derivatives
What are the critical numbers of the following equation?
f(x)=3x3+2x2
  1. x=-49,0
  2. x=49,0
  3. x=-94,0
  4. x=94,0
Grade 12 Integrals
What is the indefinite integral of f(x)=3x3+2x2?
  1. ∫3x3+2x2dx=3x44+2x33+C
  2. ∫3x3+2x2dx=9x2+4x+C
  3. ∫3x3+2x2dx=3x3+2x2+C
  4. ∫3x3+2x2dx=4x33+3x22+C
Grade 12 Limits
What is limx→∞1ex?
  1. -∞
  2. 0
  3. e
  4. ∞
Grade 12 Derivatives
Identify and classify the extrema of the given function.
f(x)=x3+x2-x
  1. Relative maximum: (-1,32); relative minimum: (13,-1)
  2. Relative maximum: (-1,1); absolute minimum: (13,-527)
  3. Relative maximum: (-1,1); relative minimum: (13,-527)
  4. Relative maximum: (-1,32); no relative or absolute minimums
Grade 12 Derivatives
An equation of the line tangent to the graph of y=cos(2x) at x=π4 is which of the following?
  1. y-1=-(x-π4)
  2. y-1=-2(x-π4)
  3. y=2(x-π4)
  4. y=-(x-π4)
  5. y=-2(x-π4)
Grade 12 Derivatives
f(x)=2x5+x3-3x is
  1. increasing on (-∞,∞).
  2. decreasing on (-∞,-0.65)∪(0.65,∞) and increasing on (-0.65,0.65).
  3. increasing on (-∞,-0.65)∪(0.65,∞) and decreasing on (-0.65,0.65).
  4. decreasing on (-∞,-1.4)∪(1.4,∞) and decreasing on (1.4,-1.4).
Grade 12 Integrals
Find the indefinite integral. ∫csc(x2-2)cot(x2-2)x dx
  1. 12tan(x2-2)+C
  2. cot(x2-2)+C
  3. -12csc(x2-2)+C
  4. -sec(x2-2)+C
Grade 12 Derivatives
Find the derivative for this function: f(x)=x2+5x+3.
  1. f′(x)=2x+5
  2. f′(x)=2x+3
  3. f′(x)=2x+5x
Grade 12 Derivatives
Differentiate. f(x)=x-32
  1. f′(x)=x-52
  2. f′(x)=-32x-52
  3. f′(x)=-32x-12
  4. f′(x)=-23x-2
Grade 12 Derivatives
Differentiate. f(x)=3x-2+5x-3-2x-5
  1. f′(x)=-6x-1-15x-2+10x-4
  2. f′(x)=3x-3+5x-4-2x-6
  3. f′(x)=3x-1+5x-2-2x-4
  4. f′(x)=-6x-3-15x-4+10x-6
Grade 12 Integrals
Find the indefinite integral. ∫3x2dx
  1. 6x+C
  2. x3+C
  3. 12x+C
  4. 23x3+C
Grade 12 Integrals
Find the indefinite integral. ∫cos4(x)sin(x) dx
  1. cos5(x)+C
  2. -15sin5(x)+C
  3. sin5(x)+C
  4. -15cos5(x)+C
  5. -5cos5(x)+C
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