Consider the function\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{sin2x}}{{5x}}\;\;\;\;\;\;\;\;\;if\;x \ne 0\;\;\;\;\;\;\;\;\;\;}\\ {\frac{2}{{15}}\;\;\;\;\;if\;x = 0} \end{array}} \right.\)Which one of the following is correct in respect of the function?

Consider the function\(f\left( x \right) = \left\{ {\begin{array}{*{20

1.	Consider the function\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{sin2x}}{{5x}}\;\;\;\;\;\;\;\;\;if\;x \ne 0\;\;\;\;\;\;\;\;\;\;}\\ {\frac{2}{{15}}\;\;\;\;\;if\;x = 0} \end{array}} \right.\)Which one of the following is correct in respect of the function?
A.	It is not continuous at x = 0
B.	it is continuous at every x
C.	It is not continuous at x = π
D.	It is continuous at x = 0
Answer» B. it is continuous at every x

Discussion

No Comment Found

Related MCQs

If f(x) \( = \left\{ {\begin{array}{*{20}{c}} {\rm x;if\;x\;is\;rational}\\ { \rm- x;if\;x\;is\;irrational} \end{array}} \right.\), then which of the following statement is true:
If f(4) = 4, f '(4) = 1, then \(\displaystyle\lim_{x \rightarrow 4} \dfrac{2- \sqrt{f(x)}}{2-\sqrt x}\) is equal to:
If the function \(f(x)=\dfrac{2x-\sin^{-1}x}{2x+\tan^{-1}x}, x\neq 0\) is continuous at each point of its domain, then the value of f(0) is:
\(\mathop {{\rm{lim}}}\limits_{{\rm{x}} \to 1 - } \frac{{\sqrt {\rm{\pi }} - \sqrt {2{\rm{si}}{{\rm{n}}^{ - 1}}{\rm{x}}} }}{{\sqrt {1 - {\rm{x}}} }}{\rm{\;}}\)is equal to
\(\mathop {\lim }\limits_{y \to a} (\sin \frac{{y - a}}{2}\tan \frac{{\pi y}}{{2a}})\) is equal to
\(\mathop {{\rm{lim}}}\limits_{{\rm{n}} \to - \infty } \left( {\frac{{\rm{n}}}{{{{\rm{n}}^2} + {1^2}}} + \frac{{\rm{n}}}{{{{\rm{n}}^2} + {2^2}}} + \frac{{\rm{n}}}{{{{\rm{n}}^2} + {3^2}}} + \ldots + \frac{1}{{5{\rm{n}}}}} \right)\) is equal to
If\(\;{\rm{f}}\left( {\rm{x}} \right) = \left[ {\rm{x}} \right] - \left[ {\frac{{\rm{x}}}{4}} \right]\) , x ∈ R, where [x] denotes the greatest integer function, then:
If \(f\left( x \right) = \sqrt {25 - {x^2},} \) then what is \(\mathop {\lim }\limits_{x \to 1} \frac{{f\left( x \right) - f\left( 1 \right)}}{{x - 1}}\) equal to?
Let S be the set of all values offor which the tangent to the curvey = f(x) = x3 – x2 – 2x at (x, y) is parallel to the line segment joining the points (1, f(1)) and (-1, f(-1)), then S is equal to:
\(\mathop {{\rm{lim}}}\limits_{{\rm{y}} \to 0} \frac{{\sqrt {1 + \sqrt {1 + {{\rm{y}}^4}} } - \sqrt 2 }}{{{{\rm{y}}^4}}}\)

Consider the function\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{sin2x}}{{5x}}\;\;\;\;\;\;\;\;\;if\;x \ne 0\;\;\;\;\;\;\;\;\;\;}\\ {\frac{2}{{15}}\;\;\;\;\;if\;x = 0} \end{array}} \right.\)Which one of the following is correct in respect of the function?

Discussion

No Comment Found

Related MCQs

Reply to Comment