1. What is the derivative of the function f(x) = 3x^2 with respect to x?
A) 6x
B) 3x^2
C) 6x^2
D) 9x
Answer: A) 6x
2. What is the integral of the function f(x) = 2x with respect to x?
A) x^2
B) x^2 + C
C) 2x^2
D) x^3
Answer: B) x^2 + C (where C is the constant of integration)
3. What is the derivative of the constant function f(x) = 5?
A) 0
B) 1
C) 5
D) -5
Answer: A) 0
4. What is the limit of the function lim(x->2) (3x + 1)?
A) 5
B) 7
C) 8
D) 6
Answer: B) 7
5. What is the derivative of the function f(x) = sin(x)?
A) cos(x)
B) -cos(x)
C) sin(x)
D) -sin(x)
Answer: A) cos(x)
6. What is the integral of the function f(x) = 3x^2 with respect to x?
A) x^2 + C
B) x^3 + C
C) x^3
D) 3x^3
Answer: B) x^3 + C (where C is the constant of integration)
7. What is the derivative of the function f(x) = e^x?
A) e^x
B) -e^x
C) ln(x)
D) 1/x
Answer: A) e^x
8. What is the limit of the function lim(x->3) (x^2 – 9) / (x – 3)?
A) 6
B) 9
C) 3
D) Does not exist
Answer: C) 3
9. What is the integral of the function f(x) = cos(x) with respect to x?
A) sin(x)
B) -sin(x)
C) cos(x)
D) -cos(x)
Answer: B) -sin(x) + C (where C is the constant of integration)
10. What is the derivative of the function f(x) = ln(x)?
A) 1/x
B) x
C) -1/x
D) e^x
Answer: A) 1/x
11. What is the limit of the function lim(x->0) (sin(x) / x)?
A) 1
B) 0
C) -1
D) Does not exist
Answer: A) 1
12. What is the integral of the function f(x) = 1/x with respect to x?
A) ln(x)
B) -ln(x)
C) x^2 / 2
D) -1/x
Answer: A) ln(x) + C (where C is the constant of integration)
13. What is the derivative of the function f(x) = x^3 + 2x^2 – 5x + 7?
A) 3x^2 + 4x – 5
B) x^2 + 4x – 5
C) 3x^2 + 4x + 5
D) x^2 + 4x + 5
Answer: A) 3x^2 + 4x – 5
14. What is the limit of the function lim(x->∞) (1/x)?
A) 0
B) ∞
C) 1
D) -∞
Answer: A) 0
15. What is the integral of the function f(x) = e^x with respect to x?
A) e^x
B) -e^x
C) e^x + C
D) ln(x)
Answer: C) e^x + C (where C is the constant of integration)
16. What is the derivative of the function f(x) = 2cos(x) – 3sin(x)?
A) -2cos(x) – 3sin(x)
B) 2cos(x) – 3sin(x)
C) -2sin(x) – 3cos(x)
D) 2sin(x) – 3cos(x)
Answer: B) 2cos(x) – 3sin(x)
17. What is the derivative of the function f(x) = cos(x) + 2x^3 – 5?
A) -sin(x) + 6x^2
B) -sin(x) + 6x^2 + 1
C) -sin(x) + 6x^3 – 5
D) -sin(x) + 6x^2 – 5
Answer: A) -sin(x) + 6x^2
18. What is the integral of the function f(x) = 4x^3 – 2x + 7 with respect to x?
A) x^4 – x^2 + 7x + C
B) x^4 – x^2 + 7x^2 + C
C) x^4 – x^2 + 7x + 7C
D) x^4 – x^2 + 7 + C
Answer: A) x^4 – x^2 + 7x + C
19. What is the derivative of the function f(x) = e^x + ln(x) + 3x^2?
A) e^x + 1/x + 6x
B) e^x + 1/x + 3x^2
C) e^x + 1/x + 2x^2
D) e^x + 1/x + 5x^2
Answer: A) e^x + 1/x + 6x
20. What is the integral of the function f(x) = 1/x + sin(x) with respect to x?
A) ln(x) – cos(x) + C
B) ln(x) – cos(x) – C
C) ln(x) + cos(x) + C
D) ln(x) + cos(x) – C
Answer: A) ln(x) – cos(x) + C
21. What is the derivative of the function f(x) = x^2 + 1?
A) x
B) x^2 + 1
C) 2x
D) 2x^2
Answer: C) 2x
22. What is the integral of the function f(x) = 2x + cos(x) with respect to x?
A) 2ln(x) + sin(x) + C
B) 2ln(x) + sin(x) – C
C) 2ln(x) – sin(x) + C
D) 2ln(x) – sin(x) – C
Answer: A) 2ln(x) + sin(x) + C
23. What is the derivative of the function f(x) = sin(x)/x + e^x?
A) xcos(x) – sin(x)/x^2 + e^x
B) xcos(x) + sin(x)/x^2 + e^x
C) xcos(x) + sin(x)/x + e^x
D) xcos(x) – sin(x)/x + e^x
Answer: D) xcos(x) – sin(x)/x + e^x
24. What is the integral of the function f(x) = 1/x^2 + tan(x) with respect to x?
A) -1/x + ln|cos(x)| + C
B) -1/x + ln|cos(x)| – C
C) -1/x – ln|cos(x)| + C
D) -1/x – ln|cos(x)| – C
Answer: A) -1/x + ln|cos(x)| + C
25. What is the derivative of the function f(x) = x^3 ln(x) + e^x?
A) 3x^2 ln(x) + x^2 + e^x
B) 3x^2 ln(x) + x^3 + e^x
C) 3x^2 ln(x) + x^3 ln(x) + e^x
D) 3x^2 ln(x) + x^3 ln(x) + e^x + x^2
Answer: C) 3x^2 ln(x) + x^3 ln(x) + e^x
26. What is the integral of the function f(x) = cos(x)/x^2 + 1/x with respect to x?
A) -cos(x)/x + ln|x| + C
B) -cos(x)/x – ln|x| + C
C) cos(x)/x + ln|x| + C
D) -cos(x)/x – ln|x| – C
Answer: A) -cos(x)/x + ln|x| + C
27. What is the derivative of the function f(x) = ln(x^2 + 1)?
A) 2x / (x^2 + 1)
B) x / (x^2 + 1)
C) 2x / (x^2 + 1)^2
D) 1 / (x^2 + 1)
Answer: A) 2x / (x^2 + 1)
28. What is the integral of the function f(x) = e^x/x with respect to x?
A) Ei(x) + C
B) e^x/x + C
C) e^x + C
D) -e^x/x + C
Answer: A) Ei(x) + C (where Ei(x) is the Exponential Integral function)
29. What is the derivative of the function f(x) = 2x – e^x?
A) 2 – e^x
B) 2x – e^x
C) 2 – e^x
D) -2 – e^x
Answer: A) 2 – e^x
30. What is the integral of the function f(x) = e^(-x^2) with respect to x?
A) √π erf(x) + C
B) e^(-x^2) + C
C) √π erf(x) – C
D) e^(-x^2) / 2 + C
Answer: A) √π erf(x) + C (where erf(x) is the Error Function)
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