Home › TS EAMCET › Mathematics › Limits and Continuity › After expanding eˣ as a power series, (eˣ − 1 − …
After expanding eˣ as a power series, (eˣ − 1 − x)/x² has which limit at 0?
A1/2
B0
C2
D1
Answer & Solution
Correct answer: A. 1/2
Using eˣ = 1 + x + x²/2 + higher terms, the ratio tends to 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?Define f(x) = (1 − cos x)/x² off zero. Continuity at 0 needs f(0) equal to what?