Functions and Relations MCQs with Answers

Find $\lim_{x \to 1^+} \left(2 + \sqrt{x - 1}\right) =$ ?

• A.Does not exist
• B.$3$
• C.$1$
• D.$2$

Mean Value Theorem is applied to _ functions.

• A.Continuous
• B.Differentiable
• C.Both A and B
• D.None of these

What is the derivative of $\sin^2 x$?

• A.$\cos^2 x$
• B.$2\sin x$
• C.$\sin(2x)$
• D.$2\cos x$

If $f(x) = 5$, then $f'(x)$ at $x = 1$ is?

• A.Does not exist
• B.$5$
• C.$1$
• D.$0$

If a variable $y$ depends upon a variable $x$ in such a way that each value of $x$ determines exactly one value of $y$, then we say that

• A.$y$ is a function of $x$
• B.$x$ is a function of $y$
• C.$x$ and $y$ are independent variables
• D.$y$ is a constant multiple of $x$

What is the derivative of $f(x) = x^2 \cdot \sin(x)$?

• A.$2x \cdot \sin(x) - x^2 \cdot \cos(x)$
• B.$2x \cdot \cos(x)$
• C.$x^2 \cdot \cos(x) - 2x \cdot \sin(x)$
• D.$2x \cdot \sin(x) + x^2 \cdot \cos(x)$

If the limit $\lim_{h \to 0} \frac{f(x+h,\, y) - f(x,\, y)}{h}$ exists, it is called the partial derivative of $f$ with respect to _?

• A.$x$ at $(x, y)$
• B.$y$ at $(x, y)$
• C.$h$ at $(x, y)$
• D.Both $x$ and $y$

The hyperbolic function $y$ is equal to _?

• A.$\frac{e^y - e^{-y}}{2}$
• B.$\frac{e^y + e^{-y}}{e^y - e^{-y}}$
• C.$\frac{e^y - e^{-y}}{e^y + e^{-y}}$
• D.$\frac{e^y + e^{-y}}{2}$

In topology, isometric metric spaces represent which kind of relation?

• A.Equivalence
• B.Partial order
• C.Strict total order
• D.None of these

The derivative of $\sin(x)$ with respect to $x$ is?

• A.$\cos(x)$
• B.$-\cos(x)$
• C.$\sin(x)$
• D.$-\sin(x)$