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Contents in Sameer Bansal Calculus Pdf
In this PDF book, There are a total of 9 chapters. They are the Given below:
- Functions
- Inverse Trigonometric Functions
- Limits, Continuity, and Differentiability
- Methods of Differentiation
- Indefinite Integration
- Definite Integration
- Application of Derivatives
- Differential Equations
- Area Under Curve
Important Questions of Calculus
What is the derivative of the function f(x) = cos(x)?
A) -sin(x)
B) sin(x)
C) -cos(x)
D) cos(x)
Ans. A) -sin(x)
What is the integral of the function ∫(4e^x + 3/x) dx?
A) 4e^x + 3ln(x) + C
B) 4e^x + 3/x + C
C) 4e^x + 3/x^2 + C
D) 4e^x + 3x + C
Ans. A) 4e^x + 3ln(x) + C (where C is the constant of integration)
What is the slope of the tangent line to the curve y = ln(x) at the point (1, 0)?
A) 0
B) 1
C) -1
D) Undefined
Ans. B) 1
If f(x) = 2x^3 – 5x^2 + 4x – 1, what is the local maximum value of the function?
A) 2
B) -5
C) 4
D) 1
Ans. C) 4
What is the second derivative of the function f(x) = e^x * sin(x)?
A) e^x * sin(x)
B) e^x * cos(x)
C) e^x * (cos(x) – sin(x))
D) e^x * (cos(x) + sin(x))
Ans. B) e^x * cos(x)
Which of the following statements is true about the integral of an odd function over a symmetric interval?
A) The integral is always zero.
B) The integral is always positive.
C) The integral is always negative.
D) The integral depends on the specific function.
Ans. A) The integral is always zero.
What is the limit of the function lim (x -> 1) [(x^2 – 1)/(x – 1)]?
A) 0
B) 1
C) 2
D) Undefined
Ans. C) 2
If a function f(x) is concave upward on an interval, which statement about its second derivative is true?
A) The second derivative is positive.
B) The second derivative is negative.
C) The second derivative is zero.
D) The second derivative is undefined.
Ans. A) The second derivative is positive.
Calculus Questions
What is the area between the curves y = x^2 and y = 2x on the interval [0, 2]?
A) 1/3
B) 4/3
C) 2/3
D) 8/3
Ans. B) 4/3
If f(x) = x^4 – 3x^2 + 2x – 7, what is the local minimum value of the function?
A) -7
B) -6
C) -5
D) -4
Ans. A) -7
What is the derivative of the function f(x) = ln(2x + 1)?
A) 1/(2x + 1)
B) 2/(2x + 1)
C) 1/(x + 1)
D) 2x
Ans. A) 1/(2x + 1)
What is the integral of the function ∫(5x^4 – 2x^3 + 3x^2) dx?
A) x^5 – (x^4)/2 + x^3 + C
B) x^5 – x^4 + x^3 + C
C) (x^5)/5 – (x^4)/4 + (x^3)/3 + C
D) (x^5)/5 – (x^4)/2 + (x^3)/3 + C
Ans. D) (x^5)/5 – (x^4)/2 + (x^3)/3 + C (where C is the constant of integration)
What is the limit of the function lim (x -> 0) (sin(1/x))?
A) 0
B) 1
C) -1
D) Undefined
Ans. D) Undefined
If f(x) = x^3 + 2x^2 – 3x + 4, what is the inflection point of the function?
A) (1, 4)
B) (-1, 6)
C) (2, 5)
D) (0, 4)
Ans. B) (-1, 6)
What is the second derivative of the function f(x) = ln(x^2)?
A) 2/x
B) 2ln(x)
C) 2x
D) 0
Ans. A) 2/x
Which of the following is the definition of the definite integral of a function f(x) from a to b?
A) ∫[a, b] f(x) dx = F(b) – F(a) where F(x) is the derivative of f(x).
B) ∫[a, b] f(x) dx = F(b) + F(a) where F(x) is the antiderivative of f(x).
C) ∫[a, b] f(x) dx = F(b) – F(a) where F(x) is the integral of f(x).
D) ∫[a, b] f(x) dx = F(b) + F(a) where F(x) is the derivative of f(x).
Ans. A) ∫[a, b] f(x) dx = F(b) – F(a) where F(x) is the derivative of f(x).
Details of the pdf of Sameer Bansal Calculus
| Book Name | Problems In Calculus For JEE |
| Author Name | Sameer Bansal |
| Pdf Language | English |
| Pdf Size | 48 MB |
| Total Pages | 270 |
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