Question
The function $\text{f(x)}=\sin^{-1}(\cos\text{x})$ is:
- Discontinuous at x = 0
- Continuous at x = 0
- Differentiable at x = 0
- None of these.
✓
Answer
- Continuous at x = 0
$\text{f(x)}=\sin^{-1}(\cos\text{x})$
$\text{f(x)}=\sin^{-1}\Big[\sin\Big(\frac{\pi}{2}-\text{x}\Big)\Big]$
$\text{f(x)}=\frac{\pi}{2}-\text{x}$
Function is continuous at x = 0.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Choose the correct answer from the given four options.
Let A = {1, 2, 3} and consider the relation R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is:
Let A = {1, 2, 3} and consider the relation R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is:
- Reflexive but not symmetric.
- Reflexive but not transitive.
- Symmetric and transitive.
- Neither symmetric, nor transitive.
The area of the region bounded by the curves y =| x – 2 |, x = 1, x = 3 and the x-axis is:
- 4
- 2
- 3
- 1
Choose the correct answer from the given four options.
The area of the quadrilateral ABCD, where A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2), is equal to:
The area of the quadrilateral ABCD, where A(0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2, 6, 2), is equal to:
- 9 sq. units.
- 18 sq. units.
- 27 sq. units.
- 81 sq. units.
Objective function of a LPP is:
- a constraint
- a function to be optimized
- a relation between the variables
- none of these
The point on the curve $y = x^2 - 3x + 2$ where tangent is perpendicular to $y = x$ is:
→If $\Delta=\left|\begin{array}{lll}5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3\end{array}\right|$, write the minor of the element $a_{23}$.
→The order and degree of the differential equation $\Big(1+3\frac{\text{dy}}{\text{dx}}\Big)^\frac{2}{3}=4\frac{\text{d}^3\text{y}}{\text{dx}^3}$ are:
→- $1,\frac{2}{3}$
- $3,1$
- $1,2$
- $3,3$
Let A = {x : -1 ≤ x ≤ 1} and f : A → A is a function defined by f(x) = x |x| then f is:
- A bijection.
- Injection but not surjection.
- Surjection but not injection.
- Neither injection nor surjection.
The feasible region for an LPP is shown below: Let $z=3 x-4 y$ be the objective function. Minimum of $z$ occurs at
→If the order of a matrix is 20 × 5 then the number of elements in the matrix is _____?
- 5
- 20
- 50
- 100