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Calculus Questions - All Grades

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Grade 12 Integrals
Find the indefinite integral. tan(8x)8 dx
  1. -8ln|cos8x|+C
  2. ln|sec8x|+C
  3. 18ln|cos8x|+C
  4. -ln|cos8x|+C
Grade 12 Derivatives
Find ddx(lne2x).
  1. 1e2x
  2. 2e2x
  3. 2x
  4. 1
  5. 2
Grade 12 Integrals
Find the indefinite integral. 4x2x2-1 dx
  1. (2x2-1)2+C
  2. ln2x2+C
  3. ln|2x2-1|+C
  4. 2(2x2-1)2+C
Grade 12 Integrals
Find the indefinite integral. cot(3x4+5)12x3 dx
  1. ln|sin3x4|+C
  2. ln|sin(3x4+5)|+C
  3. ln|sin12x3|+C
  4. ln|sin(12x3+5)|+C
Grade 12 Derivatives
Find dydx if ycosx=1.
  1. ysinx
  2. ytanx
  3. ycosx
  4. ycotx
Grade 12 Derivatives
If x2+y2=81, find dydx.
  1. -81xy
  2. -xy
  3. -81yx
  4. -yx
Grade 12 Derivatives
If sin(x+y)=log(x+y) then dydx=
  1. tan(x+y)
  2. log[tan(x+y)]
  3. -1
  4. 1
Grade 12 Derivatives
Grade 12 Derivatives
Determine the intervals of increase and decrease. f(x)=x2x2-1
  1. Increasing on (-,0) and decreasing on (0,)
  2. Increasing on (-2,0)(2,) and decreasing on (-,-2)(0,2)
  3. Increasing on (-,-1)(1,) and decreasing on (-1,1)
  4. Increasing on (-,-1)(-1,0) and decreasing on (0,1)(1,)
Grade 12 Derivatives
If y=x2ex, then dydx=
  1. 2xex
  2. x(x+2ex)
  3. xex(x+2)
  4. 2x+ex
  5. 2x+e
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