alleryStart learning →lim_(x→0) (e^x - 1)/x =
- e
- Indeterminate
- 1
- 0
Show answer and solution
Correct answer: C. 1
By l'Hôpital or Taylor: e^x ≈ 1 + x + x²/2 + ...
So (e^x - 1)/x ≈ 1 + x/2 + ...
→ 1 as x → 0. (Equivalent to d/dx(e^x) at x = 0 = e⁰ = 1.)
Indian Navy INET Limits and Continuity — practice questions
Explore 51 free Limits and Continuity questions in Indian Navy INET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 1–30 of 51.
lim_(x→0) (e^x - 1)/x =Read the answer and worked solution →What does the sign of f ′(x) tell you?Read the answer and worked solution →Complete the definition of a critical pointRead the answer and worked solution →Order the first derivative testRead the answer and worked solution →Match each sign change to its verdictRead the answer and worked solution →The second derivative testRead the answer and worked solution →True or false: maxima and minimaRead the answer and worked solution →Order the working rule for absolute maxima and minimaRead the answer and worked solution →Tap every point you must test for an absolute maximumRead the answer and worked solution →Local or absolute?Read the answer and worked solution →Complete the rate of change statementRead the answer and worked solution →The chain rule for related ratesRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →True or false: increasing and decreasingRead the answer and worked solution →Flip and pair: symbol with meaningRead the answer and worked solution →Match each situation to the right toolRead the answer and worked solution →Tap every statement true of a local maximum at cRead the answer and worked solution →Reading the tests backRead the answer and worked solution →Which test is being described?Read the answer and worked solution →Assertion and reason: rates of changeRead the answer and worked solution →Spot the odd oneRead the answer and worked solution →Complete the second derivative testRead the answer and worked solution →True or false: scope of this chapterRead the answer and worked solution →Match each kind of matrix to its conditionRead the answer and worked solution →Sort each matrix by its shapeRead the answer and worked solution →Tap every matrix that must be squareRead the answer and worked solution →Complete the definition of a matrixRead the answer and worked solution →
Worked practice questions
What does the sign of f ′(x) tell you?
Read exercise and reference answers
- Items
- Item
- f ′(x) > 0 throughout
- Category
- Increasing
- Item
- x₁ < x₂ gives f(x₁) < f(x₂)
- Category
- Increasing
- Item
- f ′(x) < 0 throughout
- Category
- Decreasing
- Item
- x₁ < x₂ gives f(x₁) > f(x₂)
- Category
- Decreasing
- Item
- f(x) = c for all x
- Category
- Constant
- Item
- f ′(x) = 0 throughout the interval
- Category
- Constant
- Categories
- Item
- Increasing
- Item
- Decreasing
- Item
- Constant
Your syllabus gives f ′(x) ≥ 0 on an interval as the test for increasing and f ′(x) ≤ 0 for decreasing.
Everything else in the chapter builds on reading that sign.
Source: syllabus Maths Part I, Ch 6 Application of Derivatives.
Complete the definition of a critical point
Read exercise and reference answers
- Missing parts
- Answer
- 0
- Choices
- 0
- 1
- undefined
- Answer
- not differentiable
- Choices
- not differentiable
- not continuous
- not defined
- Complete the statement
- A point c in the domain of f is a critical point if either f ′(c) = {0}, or f is {1} at c.
Your syllabus's definition covers two cases, and the second one is the one people forget. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.
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