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Twelfth Grade (Grade 12) Calculus Questions

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Grade 12 Derivatives
Find dydxify=3x23-4x12-2.
  1. 2x13-2x-12
  2. 3x-13-2x-12
  3. 95x53-8x32+C
  4. 2x-13-2x-12
Grade 12 Integrals
Find the indefinite integral. ∫5cos5x dx
  1. ln|sec5x+tan5x|+C
  2. ln|csc5x+cot5x|+C
  3. ln|tan5x|+C
  4. ln|sec5x|+C
Grade 12 Derivatives
Find f′(x) if f(x)=sinxcotx.
  1. cos x
  2. -sin x
  3. sin x
  4. -cos x
  5. 0
Grade 12 Derivatives
If f(x)=lnxx, for all x>0, which of the following is true?
  1. f is increasing for all x greater than 0
  2. f is increasing for all x greater than 1
  3. f is decreasing for all x between 0 and 1
  4. f is decreasing for all x between 1 and e
  5. f is decreasing for all x greater than e
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
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