Limits, Continuity & Differentiability : AIEEE Problems

Free Math Problems, Questions, Answers, Shortcuts listed topicwise

Real - valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions. Limits, continuity and differentiability. Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order upto two. Rolle's and Lagrange's Mean Value Theorems. Applications of derivatives: Rate of change of quantities, monotonic - increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normals.

List of Sample Problems

1. Question 1: f(1) = 4; f '(x) > 3 for x belongs to (0, 10), then f(5) __________
   1. has to be less than 16
   2. has to be greater than 16
   3. can be any number greater than 4
   4. should lie between 4 and 20
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2. Question 2: f(x) is a second degree polynomial such that f(1) = f(-1), then _________
   1. f '(x) should always be negative
   2. f(x) is an ever-increasing function
   3. f(2) need not be equal to f(-2)
   4. None of the above
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3. Question 3: f(x) = [x²] - [x]². Then ______
   1. f(x) cannot be negative
   2. f(x) can be discontinuous only at points where x is integral
   3. for x belongs to [3,4], f(x) can take 7 distinct values
      
      
   1. All three are true
   2. A alone is true
   3. C alone is true
   4. A and c are true
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4. Question 4:f(x) = min[x, x²], which of the following is not true
   1. f(x) is not differentiable at all values of x
   2. f '(x) = 1 for x>1
   3. f(x) is a discontinuous function
   4. f(25) = 25
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AIEEE Math Problems, Practice Questions and Answers : Listed Topicwise

Sets, Relations & Functions		Permutation Combination		Sequences & Series
Limits, Continuity & Differentiability		Statistics & Probability		Trigonometry
Mathematical Reasoning