alleryStart learning →For f(x) = |x|/x, the limit as x approaches 0
- equals 0
- does not exist
- equals 1
- equals -1
Show answer and solution
Correct answer: B. does not exist
The one-sided limits are -1 and 1, which are unequal, so no two-sided limit exists.
CA Foundation Sets, Relations and Functions — practice questions — page 3
Explore 74 free Sets, Relations and Functions questions in CA Foundation Quantitative Aptitude. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 61–74 of 74.
For f(x) = |x|/x, the limit as x approaches 0Read the answer and worked solution →If the left and right limits at p exist but differ, thenRead the answer and worked solution →The arrow written below the limit symbol in modern notation is due toRead the answer and worked solution →A function continuous on an open interval must be continuousRead the answer and worked solution →The function f(x) = 1/(x - 5) is discontinuous at x equal toRead the answer and worked solution →A polynomial function is continuousRead the answer and worked solution →Let f(x) = (x^2 - 9)/(x - 3) for x not equal to 3. For f to be continuous at 3, f(3) must beRead the answer and worked solution →f(x) = kx + 1 for x <= 2 and f(x) = 3 for x > 2 is continuous at 2 when k isRead the answer and worked solution →Let f(x) = x^2 for x < 1 and f(x) = 2x - 1 for x >= 1. At x = 1, f isRead the answer and worked solution →A function is continuous at c if the limit of f(x) as x tends to c equalsRead the answer and worked solution →For f(x) = |x|, the left limit, right limit and f(0) at x = 0 are allRead the answer and worked solution →As x tends to infinity, (3x^2 - 5)/(6x^2 + x) approachesRead the answer and worked solution →The limit of (sqrt(x) - 2)/(x - 4) as x approaches 4 isRead the answer and worked solution →As x grows large, (4x^3 + x)/(2x^3 - 7) tends toRead the answer and worked solution →
Worked practice questions
If the left and right limits at p exist but differ, then
- f is continuous at p
- the limit at p is their sum
- the limit equals f(p)
- there is no limit at p
Show answer and solution
Correct answer: D. there is no limit at p
A two-sided limit needs both one-sided limits to be equal, so unequal ones mean no limit.
The arrow written below the limit symbol in modern notation is due to
- Isaac Newton
- Henri Lebesgue
- John Venn
- G.H. Hardy
Show answer and solution
Correct answer: D. G.H. Hardy
Hardy introduced the arrow under lim in his 1908 book on pure mathematics.
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