Question 1

Function f(x) is exist when:&#10;A)LHL = RHL&#10;B)LHL ? RHL&#10;C)LHL > RHL&#10;D)LHL < RHL

Accepted Answer

For a function $f(x)$ to exist at a point, the left-hand limit (LHL) and the right-hand limit (RHL) at that point must be equal. This ensures the function is continuous at that point.

Question 2

A function expressed directly in terms of the dependent variable is an _________ function, where one variable is dependent on the other.&#10;A)implicit&#10;B)fixed&#10;C)variable&#10;D)explicit

Accepted Answer

An explicit function is one where the dependent variable is expressed directly in terms of the independent variable(s).

Question 3

In the equation y = f (x), y is the __________variable and x is the ____________variable.&#10;A)dependent; independent&#10;B)independent; dependent&#10;C)first; second&#10;D)explicit; implicit

Accepted Answer

In the equation y = f(x), y is the dependent variable because its value depends on the value chosen for x. x is the independent variable because its value is chosen freely, determining the value of y.

Question 4

The derivative of x3 is A)3x B)3 C)3x² D)x

Accepted Answer

The derivative of x^3 with respect to x is found using the power rule, which states that the derivative of x^n is n*x^(n-1). Applying this rule, the derivative of x^3 is 3*x^(3-1) = 3x^2.

Question 5

The derivative of (5x - 2)³ is A)15(5x - 2)² B)5x - 2 C)15(5x - 2)³ D)15x - 2

Accepted Answer

The derivative of a function $f(x) = (5x - 2)^{13}$ with respect to $x$ is found using the chain rule. The derivative is $f'(x) = 13(5x - 2)^{12} \cdot 5 = 15(5x - 2)^{12}$, which matches option A.

Question 6

The derivative of 2x+3 is&#10;A)x&#10;B)3&#10;C)2&#10;D)1

Accepted Answer

The derivative of a constant is 0, and the derivative of x with respect to x is 1. Therefore, the derivative of 2x is 2, and the derivative of a constant (like 3) is 0.

Question 7

A square matrix in which every non-diagonal is zero and all diagonal elements are equal is called&#10;A)Scaler matrix&#10;B)Square matrix&#10;C)Column matrix&#10;D)Row matrix

Accepted Answer

A scalar matrix is a square matrix in which all the elements of the principal diagonal are equal, and all other elements are zero.

Question 8

Differential calculus helps to find the&#10;A)Rate of change of a quantity&#10;B)Quantity when the rate of change is known&#10;C)Quantity when the rate of change is unknown&#10;D)None of the above

Accepted Answer

Differential calculus is primarily concerned with the concept of the derivative, which represents the rate of change of a quantity with respect to another variable.

Question 9

Integral calculus helps to find the&#10;A)Rate of change of a quantity&#10;B)Quantity when the rate of change is known&#10;C)Quantity when the rate o change is unknown&#10;D)None of the above

Accepted Answer

Integral calculus is primarily used to find the total quantity (such as area, volume, or some other accumulative measure) when the rate of change of that quantity with respect to another variable is known.

Question 10

A function expressed directly in terms of the dependent variable is said to be an&#10;A)Explicit function&#10;B)One valued function&#10;C)Two valued function&#10;D)None of the above

Accepted Answer

The answer of A function expressed directly in terms of...

Question 11

When the dependent variable increases with an increase in the independent variable, the function is called&#10;A)Algebraic functions&#10;B)Rational functions&#10;C)Monotonically increasing function&#10;D)None of the above

Accepted Answer

The answer of When the dependent variable increases with an...

Question 12

The limit of the ratio of the increment in the function corresponding to a small increment in the argument as the latter tends to zero is&#10;A)matrix&#10;B)limit&#10;C)function&#10;D)derivative

Accepted Answer

The answer of The limit of the ratio of the...

Question 13

Integration is also known as&#10;A)Anti-derivative&#10;B)Disintegration&#10;C)Differentiation&#10;D)Integral

Accepted Answer

The answer of Integration is also known as&#10;A)Anti-derivative&#10;B)Disintegration&#10;C)Differentiation&#10;D)Integral...

Deck 11: Fundamentals of Calculus