Calculus problem, given f (0) = 0, f '(0) = 1, f' '(0) = - 2, find LIM (x → 0) (f (x) - x) / x ^ 2 =? Given that f (0) = 0, f '(0) = 1, f' '(0) = - 2, find LIM (x → 0) (f (x) - x) / x ^ 2 =? For detailed explanation

RELATED INFORMATIONS

• 1. Calculus: Lim [(x ^ 3-x ^ 2 + X / 2) e ^ 1 / X - (x ^ 6 + 1) ^ 1 / 2] x → + ∞ It's going to be done with Taylor's remainder
• 2. LIM (x-sinx) / XLN (1 + x ^ 2) x tends to 0
• 3. If f (x) has a second derivative in the field of x = 0, and if x → 0, LIM ((SiNx + XF (x)) \ \ x3) = 1 / 2, find f (0), f '(0), f' '(0)
• 4. If f (x) has second derivative in the field of x = 0, and if x → 0, LIM ((SiNx + XF (x)) \ \ x3) = 0, find f (0), f '(0), f' '(0)
• 5. Given f (x) = (1 + x) / sinx-1 / x, let a = Lim f (x) be the value of A Given f (x) = (1 + x) / sinx-1 / x, note a = LIM (x → 0) f (x) 1. Find the value of A. answer: the value of a is 1.2. If x → 0, f (x) - A is the infinitesimal of x ^ k of the same order, find the value of constant K
• 6. lim/(x→0)⁡3*sinx/x=
• 7. Solving the limit of (1 + SiNx) ^ Cotx when x approaches 0
• 8. If the non-zero function f (x) has f (a + b) = f (a) * f (b) for any real number a and B, and if X1 proves: F (x) > 0
• 9. If the nonzero function f (x) has f (a + b) = f (a) &; f (b) for any real number A.B, and if x1, (1) prove that f (x) > 0 (2) prove that f (x) is a decreasing function (3) solve the inequality f (x-3) &; f (6-2x) ≤ 1 / 4 when f (4) = 1 / 16
• 10. If both non-zero real numbers a and B have f (a + b) = f (a) * f (b) and if x 1, we prove that f (x) is a decreasing function
• 11. Calculus problem, known Lim x → 0 f (x) / x ^ 2 = 1, find Lim x → 0 f (x) =? And then find Lim x → 0 f (x) / x =? The main problem lies in LIM x → 0, x ^ 2 = 0, and it is in the denominator position, so we can not directly think that f (x) = x ^ 2
• 12. When x approaches to 0, find the limit value of LIM (1-sinx) ^ 1 / X Very urgent, to detailed steps, trouble you The answer must be right!!
• 13. According to LIM (SiNx / x) = 1, find LIM (tan2x / x) =? X approaches 0, x approaches 0
• 14. When x approaches 0, LIM (2 ^ X-2 ^ SiNx) / x ^ 3 It's molecular. I can't pour it out
• 15. LIM (SiNx + e ^ x) ^ (1 / x) x tends to 0
• 16. The function f (x) = x + SiNx + 1, if f (a) = 2, then f (- a)=___ X belongs to R
• 17. f(x)={sinx+1(x≥0),2x-1(x
• 18. Let f (x) be continuous on [0,2], have a second derivative in (0,2), and lim (x approaches 1 / 2) = 0,2 ∫ 1,1 / 2F (x) d (x) =It is proved that there is at least one point δ in (0,2) such that f (δ) = 0
• 19. Let f (x) have the second derivative at x = X. it is proved that the limit of [f (X. + H) - 2F (X.) + F (X. - H)] / h ^ 2 at h → 0 is equal to the second derivative of F (X.)
• 20. Let the second derivative of H (x) be continuous at x = 0, and H (0) = 0, H '(0) is not equal to 0. It is proved that the curve y = f (x) = (1-cosx) H (x) is continuous at x = 0 It is proved that f (x) must have inflection point at x = 0