If\[i=\sqrt{-1}\],then\[\frac{{{e}^{xi}}+{{e}^{-xi}}}{2}=\] – McqOptions

MCQOPTIONS

1.	If\[i=\sqrt{-1}\],then\[\frac{{{e}^{xi}}+{{e}^{-xi}}}{2}=\]
A.	\[1+\frac{{{x}^{2}}}{2\,!}+\frac{{{x}^{4}}}{4\,!}+.....\infty \]
B.	\[1-\frac{{{x}^{2}}}{2\,!}+\frac{{{x}^{4}}}{4\,!}-.....\infty \]
C.	\[x+\frac{{{x}^{3}}}{3\,!}+\frac{{{x}^{5}}}{5\,!}+....\infty \]
D.	\[i\,\left[ x-\frac{{{x}^{3}}}{3\,!}+\frac{{{x}^{5}}}{5\,!}-.....\infty\right]\]
Answer» C. \[x+\frac{{{x}^{3}}}{3\,!}+\frac{{{x}^{5}}}{5\,!}+....\infty \]

Discussion

No Comment Found

Related MCQs

The value of\[{{a}^{{{\log }_{b}}x}}\], where \[a=0.2,\ b=\sqrt{5},\ x=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+.........\]to \[\infty \] is
The sum of infinity of a geometric progression is \[\frac{4}{3}\] and the first term is \[\frac{3}{4}\]. The common ratio is[MP PET 1994]
If \[a,\ b,\ c\] are \[{{p}^{th}},\ {{q}^{th}}\] and \[{{r}^{th}}\]terms of a G.P., then \[{{\left( \frac{c}{b} \right)}^{p}}{{\left( \frac{b}{a} \right)}^{r}}{{\left( \frac{a}{c} \right)}^{q}}\] is equal to
If\[i=\sqrt{-1}\],then\[\frac{{{e}^{xi}}+{{e}^{-xi}}}{2}=\]
The sum of the series \[\frac{1}{2\,!}-\frac{1}{3\,!}+\frac{1}{4\,!}-.....\] is [DCE 2002]
\[\frac{{{1}^{2}}.2}{1\,!}+\frac{{{2}^{2}}.3}{2\,!}+\frac{{{3}^{2}}.4}{3\,!}+.....\infty =\] [UPSEAT 1999]
\[1+\frac{1+2}{2\,!}+\frac{1+2+3}{3\,!}+\frac{1+2+3+4}{4\,!}+....\infty =\] [Roorkee 1999; MP PET 2003]
The sum of \[1+\frac{2}{5}+\frac{3}{{{5}^{2}}}+\frac{4}{{{5}^{3}}}+...........\]upto \[n\] terms is [MP PET 1982]
The value of \[\sum\limits_{r=1}^{n}{\log \left( \frac{{{a}^{r}}}{{{b}^{r-1}}} \right)}\] is
Let \[{{T}_{r}}\] be the \[{{r}^{th}}\] term of an A.P. for \[r=1,\ 2,\ 3,....\]. If for some positive integers \[m,\ n\] we have \[{{T}_{m}}=\frac{1}{n}\] and \[{{T}_{n}}=\frac{1}{m}\], then equals [IIT 1998]