Limit, Continuity and Differentiability
Real-valued functions, algebra of functions, polynomial, rational, trigonometric, logarithmic and exponential functions; inverse functions; graphs of simple functions; limits, continuity and differentiability; differentiation of sum, difference, product and quotient of functions; derivatives of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; Rolle's and Lagrange's mean value theorems; applications — tangents and normals, increasing and decreasing functions, maxima and minima.
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Take a full mock →Q1 · Limit, Continuity and Differentiability · EASY
Let f(x) = (x^2 - 4)/(x - 2) for x ≠ 2. If f is continuous at x = 2, then f(2) equals
Q2 · Limit, Continuity and Differentiability · EASY
If f(x) = x^3 - 3x + 5, then the number of points where the tangent to the curve y = f(x) is parallel to the x-axis is
Q3 · Limit, Continuity and Differentiability · MEDIUM
The function f(x) = |x - 1| + |x - 2| is
Q4 · Limit, Continuity and Differentiability · MEDIUM
Let f(x) = x^2 sin(1/x) for x ≠ 0 and f(0) = 0. Then at x = 0, f is
Q5 · Limit, Continuity and Differentiability · HARD
If f(x) is a differentiable function satisfying f(1) = 2 and f'(x) ≥ 3 for all x in [1, 5], then the minimum possible value of f(5) is