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Grade 12 College

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Calculus Questions - All Grades

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Grade 12 Limits
Describe the end behavior of f(x)=2x-3.
  1. As x→-∞,y→-3; as x→∞,y→∞
  2. As x→-∞,y→∞; as x→∞,y→∞
  3. As x→-3,y→∞; as x→∞,y→∞
  4. As x→-∞,y→∞; as x→∞,y→-3
Grade 12 Derivatives
Find the derivative. f(x)=5√x7
  1. f′(x)=5√7x6
  2. f′(x)=755√x2
  3. f′(x)=4√x6
  4. f′(x)=5√x2
Grade 12 Derivatives
Differentiate. f(x)=4x10025
  1. f′(x)=4x9925
  2. f′(x)=8x105
  3. f′(x)=x99625
  4. f′(x)=16x99
Grade 12 Limits
Evaluate. limx→-2x+2x3+8
  1. 16
  2. 112
  3. 14
  4. 0
Grade 12 Derivatives
On what intervals is the function f(x)=3x3+2x2 increasing or decreasing?
  1. Increasing: (-∞,-49)∪(0,∞), decreasing: (-49,0)
  2. Increasing: (-∞,-49), decreasing: (-49,0)
  3. Increasing: (-∞,0)∪(-49,∞), decreasing: (-49,0)
  4. Increasing: (-49,0), decreasing: (-∞,-49)∪(0,∞)
Grade 12 Limits
Evaluate the limit. limx→0(x-5)2-25x
  1. Does not Exist
  2. -10
  3. ∞
  4. 0
Grade 12 Derivatives
Find the intervals of increase and decrease for the following function. f(x)=√3x2-9x+6
  1. Increasing on (32,∞) and decreasing on (-∞,32)
  2. Increasing on (2,∞) and decreasing on (-∞,1)
  3. Increasing on (32,∞)
  4. Increasing on (2,∞)
Grade 12 Derivatives
What are all the values of x for which the function f defined by f(x)=x3+3x2-9x+7 is increasing?
  1. -3<x<1
  2. -1<x<1
  3. x<-3 and x>1
  4. x<-1 and x>3
  5. All real numbers
Grade 12 Derivatives
Identify the intervals on which the given function is increasing and decreasing.
f(x)=x2e-x2
  1. Increasing: (-∞,-1)∪(0,1); decreasing: (-1,0)∪(1,∞)
  2. Increasing: (-∞,0); decreasing: (0,∞)
  3. Increasing for all x
  4. Increasing: (-1,0)∪(1,∞); decreasing: (-∞,-1)∪(0,1)
Grade 12 Derivatives
Find ddx(tan-1(x-√a2-x2x+√a2-x2)).
  1. -1√a2-x2
  2. 1√a2-x2
  3. √a2-x2
  4. x√a2-x2
Grade 12 Limits
Is h(x)=x-4x2-5x+4 continuous or discontinuous at x = 1? Justify using continuity test. If discontinuous, what type?
  1. Continuous
  2. Infinite discontinuity
  3. Jump discontinuity
  4. Removable discontinuity
College Derivatives
What is the derivative of 21?
  1. 0
  2. 21
  3. 7
  4. 3
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