## Sameer Bansal Calculus Pdf

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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:

1. Functions
2. Inverse Trigonometric Functions
3. Limits, Continuity, and Differentiability
4. Methods of Differentiation
5. Indefinite Integration
6. Definite Integration
7. Application of Derivatives
8. Differential Equations
9. 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).