Home › TS EAMCET › Mathematics › Limits and Continuity › Define f(x) = (1 − cos x)/x² off zero. Continuit…
Define f(x) = (1 − cos x)/x² off zero. Continuity at 0 needs f(0) equal to what?
A1
B0
C2
D1/2
Answer & Solution
Correct answer: D. 1/2
The limit of (1 − cos x)/x² at 0 is 1/2, so f(0) must be 1/2.
Related questions
How many real points of discontinuity does (x + 1)/(x² − 5x + 6) have?Let f(x) = 2x + 1 for x < 2 and x² + 1 for x ≥ 2. What is the limit at x = 2?What does the differentiability of a function at a point guarantee about it there?For f(x) = x³ + x − 1, in which interval must a root lie?How many points in the open interval (0, 3) is ⌊x⌋ discontinuous at?At which of these points is tan x discontinuous?At which real number does f(x) = 1/(x − 3) break down?Take f = kx² when x ≤ 2 and f = 3 when x > 2. Continuity at 2 forces k to be what?