ECAT Pakistan · Mathematics
Functions, Limits and Calculus
9 practice questions, each with the answer and an explanation.
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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.
All 9 questions
- Evaluate the limit: lim (x -> 0) of (sin(5x) - sin(3x)) / (2x).
- Find the derivative dy/dx of the implicit function x^2 + 2xy + y^3 = 4 at the point (1, 1).
- What is the maximum value of the function f(x) = x * (12 - 2x)^2 on the interval [0, 6]?
- What is the equation of the normal to the parabola y^2 = 8x at the point (2, 4)?
- What is the domain of the real-valued function f(x) = sqrt(9 - x^2) / ln(x - 1)?
- Evaluate: lim (x -> infinity) of (1 + 3/x)^(2x).
- At what point on the curve y = x^3 - 3x is the tangent parallel to the line y = 9x + 5?
- What is the derivative of f(x) = arctan(e^(2x)) with respect to x?
- According to Rolle's Theorem, for f(x) = x^3 - 4x on [-2, 2], what is the value of c in (-2, 2) where f'(c) = 0?
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