alleryStart learning →The value of $\displaystyle\lim_{x\to 2} x^2$ is:
- 4
- 0
- 2
- $\infty$
Show answer and solution
Correct answer: A. 4
Polynomials are continuous, so the limit is the value: 2² = 4.
Indian Navy Pilot Limits and Derivatives — practice questions
Explore 5 free Limits and Derivatives questions in Indian Navy Pilot Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Limits and Derivatives with Quill →Limits and Derivatives questions and exercises with answers
Showing questions 1–5 of 5.
The value of $\displaystyle\lim_{x\to 2} x^2$ is:Read the answer and worked solution →The derivative of $x^3$ with respect to $x$ is:Read the answer and worked solution →The famous standard limit lim_{x→0} (sin x)/x (with x in radians) equals:Read the answer and worked solution →Key in the limitRead the answer and worked solution →Which one does NOT belong?Read the answer and worked solution →
Worked practice questions
The derivative of $x^3$ with respect to $x$ is:
- $x^2$
- $3x$
- $\dfrac{x^4}{4}$
- $3x^2$
Show answer and solution
Correct answer: D. $3x^2$
Power rule: d/dx(x³) = 3x².
The famous standard limit lim_{x→0} (sin x)/x (with x in radians) equals:
- $1$ (foundational standard limit)
- $0$ (assuming numerator dominates)
- $x$ (the simplification, incorrect)
- Does not exist (the limit fails)
Show answer and solution
Correct answer: A. $1$ (foundational standard limit)
lim_{x→0} (sin x)/x = 1 (x in radians).
Even though sin(0)/0 = 0/0 (indeterminate).
Proved via squeeze theorem or geometric argument.
Foundational for many sin/cos/tan limits.
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