D5-D7 Maclaurin series and limits Quiz: AQA Further Maths, Unit 2

The 20 questions

1. The Maclaurin series of e^x begins?

   • 1 - x + x^2/2! - x^3/3! + ...
   • 1 + 2x + 4x^2/2! + ...
   • 1 + x + x^2/2! + x^3/3! + ...
   • x + x^2/2! + x^3/3! + ...

2. The Maclaurin series of sin x begins?

   • x - x^2/2! + x^3/3! - ...
   • x - x^3/3! + x^5/5! - ...
   • 1 - x^2/2! + x^4/4! - ...
   • x + x^3/3! + x^5/5! + ...

3. The Maclaurin series of cos x begins?

   • 1 + x^2/2! + x^4/4! + ...
   • 1 - x + x^2/2! - ...
   • x - x^3/3! + x^5/5! - ...
   • 1 - x^2/2! + x^4/4! - ...

4. For which values of x is the Maclaurin series of ln(1 + x) valid?

   • All real x
   • -1 < x <= 1
   • x > 1 only
   • 0 <= x <= 1

5. What is the general term of the Maclaurin series of e^x?

   • x^(n+1) / n!
   • x^n / n!
   • n x^n
   • x^n / (n - 1)!

6. What is the Maclaurin series of e^(2x) up to x^2?

   • 1 + 2x + x^2
   • 1 + x + x^2/2
   • 1 + 2x + 2x^2
   • 1 + 2x + 4x^2

7. What is the limit of sin x / x as x tends to 0?

   • 1
   • 0
   • 1/2
   • infinity

8. What is the limit of (e^x - 1 - x)/x^2 as x tends to 0?

   • 1
   • 0
   • 2
   • 1/2

9. What is the limit of (1 - cos x)/x^2 as x tends to 0?

   • 1
   • -1/2
   • 1/2
   • 0

10. What is the limit of (x - sin x)/x^3 as x tends to 0?

    • 1/2
    • 0
    • 1/6
    • 1/3

11. What is the Maclaurin series of ln(1 + x) up to x^3?

    • x + x^2/2 + x^3/3
    • x - x^2 + x^3/3
    • x - x^2/2 - x^3/3
    • x - x^2/2 + x^3/3

12. What is the Maclaurin series of cos(2x) up to x^2?

    • 1 - 4x^2
    • 1 + 2x^2
    • 1 - 2x^2
    • 1 - x^2

13. What is the limit of ln(1 + 2x)/x as x tends to 0?

    • 0
    • 1
    • 1/2
    • 2

14. What is the limit of (e^x - e^(-x))/sin(2x) as x tends to 0?

    • 2
    • 0
    • 1/2
    • 1

15. What is the limit of (x - tan x)/x^3 as x tends to 0?

    • 1/3
    • -1/6
    • -1/3
    • 0

16. What is the limit of (sin x - x + x^3/6)/x^5 as x tends to 0?

    • 0
    • 1/24
    • 1/6
    • 1/120

17. What is the Maclaurin series of x e^(x^2) up to x^3?

    • x + 2x^3
    • 1 + x + x^3
    • x + x^3
    • x + x^2

18. What is the coefficient of x^4 in the Maclaurin series of cos x?

    • 1/6
    • 1/24
    • 1/4
    • -1/24

19. What is the limit of (e^x - 1)/ln(1 + x) as x tends to 0?

    • 1
    • 1/2
    • 0
    • e

20. Using l'Hopital's rule, what is the limit of ln(1 + x)/x as x tends to 0?

    • 1
    • infinity
    • 0
    • -1

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