Let \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\cos \left[ x \right],}&{x \ge 0}\\ {\left| x \right| + a,}&{x < 0} \end{array}} \right.,\) where [x] denotes the greatest integer ≤ x. If f should be continuous at x = 0, then a must be

Let \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\cos \lef

1.	Let \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\cos \left[ x \right],}&{x \ge 0}\\ {\left\| x \right\| + a,}&{x < 0} \end{array}} \right.,\) where [x] denotes the greatest integer ≤ x. If f should be continuous at x = 0, then a must be
A.	0
B.	1
C.	2
D.	-1
Answer» C. 2

Discussion

No Comment Found

Related MCQs

Consider the function f defined by \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {{x^2} - 1,}&{x < 3}\\ {2ax,}&{x \ge 3} \end{array}} \right.\) for all real numbers x. If f is continuous at x = 3, then value of a
Let f(x) be defined as follows: \({\rm{f}}\left( {\rm{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {2{\rm{x}} + 1,{\rm{\;\;}} - 3 < {\rm{x}} < - 2}\\ {{\rm{x}} - 1,{\rm{\;\;}} - 2 \le {\rm{x}} < 0}\\ {{\rm{x}} + 2,{\rm{\;\;\;}}0 \le {\rm{x}} < 1} \end{array}} \right.\) Which one of the following statements is correct in respect of the above function?
Let f: R → R be defined by \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {x\sin \left( {\frac{1}{x}} \right)}&{if\;x > 0}\\ 0&{x \le 0} \end{array}} \right.\) Then
If \({\rm{F}}\left( {\rm{x}} \right) = \sqrt {9 - {{\rm{x}}^2}} \), then what is \(\mathop {\lim }\limits_{{\rm{x}} \to 1} \frac{{{\rm{F}}\left( {\rm{x}} \right) - {\rm{F}}\left( 1 \right)}}{{{\rm{x}} - 1}}\) equal to?
\(\frac{1}{{{{\log }_2}x}} + \frac{1}{{{{\log }_3}x}} + \frac{1}{{{{\log }_4}x}} + \ldots .. + \frac{1}{{{{\log }_{50}}x}},x \ne 1\) is equal to
If \(\rm \displaystyle\lim_{x \rightarrow 1} \dfrac{x^4-1}{x-1} = \lim_{x\rightarrow k} \dfrac{x^3-k^3}{x^2-k^2}\), where k ≠ 0, then what is the value of k?
If \({\rm{G}}\left( {\rm{x}} \right) = \sqrt {(25 - {{\rm{x}}^2}} \) then what is \(\mathop {\lim }\limits_{{\rm{x}} \to 1} \frac{{{\rm{G}}\left( {\rm{x}} \right) - {\rm{G}}\left( 1 \right)}}{{{\rm{x}} - 1}}{\rm{\;}}\)equal to?
\(\displaystyle\lim_{x\rightarrow 0} \dfrac{a^x-b^x}{e^x-1}\) is equal to :
If \({\rm{f}}\left( {\rm{x}} \right) = \frac{{{\rm{sin}}\left( {{{\rm{e}}^{{\rm{x}} - 2}} - 1} \right)}}{{{\rm{In}}\left( {{\rm{x}} - 1} \right)}}\), then \(\mathop {\lim }\limits_{{\rm{x}} \to 2} {\rm{f}}\left( {\rm{x}} \right)\) is equal to
\(\mathop {{\rm{lim}}}\limits_{x \to \infty } \left( {\frac{{2 + {x^2}}}{{1 + x\;}} - Ax - B} \right) = 3\)What is the value of B?

Let \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\cos \left[ x \right],}&{x \ge 0}\\ {\left| x \right| + a,}&{x < 0} \end{array}} \right.,\) where [x] denotes the greatest integer ≤ x. If f should be continuous at x = 0, then a must be

Discussion

No Comment Found

Related MCQs

Reply to Comment