Which of the following is correct?
A. $$\mathop {\lim }\limits_{{\text{x}} \to 0} \left( {\frac{{\sin \,4{\text{x}}}}{{\sin \,2{\text{x}}}}} \right) = 1{\text{ and }}\mathop {\lim }\limits_{{\text{x}} \to 0} \left( {\frac{{\tan {\text{x}}}}{{\text{x}}}} \right) = 1$$
B. $$\mathop {\lim }\limits_{{\text{x}} \to 0} \left( {\frac{{\sin \,4{\text{x}}}}{{\sin \,2{\text{x}}}}} \right) = \infty {\text{ and }}\mathop {\lim }\limits_{{\text{x}} \to 0} \left( {\frac{{\tan {\text{x}}}}{{\text{x}}}} \right) = 1$$
C. $$\mathop {\lim }\limits_{{\text{x}} \to 0} \left( {\frac{{\sin \,4{\text{x}}}}{{\sin \,2{\text{x}}}}} \right) = 2{\text{ and }}\mathop {\lim }\limits_{{\text{x}} \to 0} \left( {\frac{{\tan {\text{x}}}}{{\text{x}}}} \right) = \infty $$
D. $$\mathop {\lim }\limits_{{\text{x}} \to 0} \left( {\frac{{\sin \,4{\text{x}}}}{{\sin \,2{\text{x}}}}} \right) = 2{\text{ and }}\mathop {\lim }\limits_{{\text{x}} \to 0} \left( {\frac{{\tan {\text{x}}}}{{\text{x}}}} \right) = 1$$
Answer: Option D
This Question Belongs to Engineering Maths >> Calculus
The Taylor series expansion of 3 sinx + 2 cosx is . . . . . . . .
A. 2 + 3x - x2 - \[\frac{{{{\text{x}}^3}}}{2}\] + ...
B. 2 - 3x + x2 - \[\frac{{{{\text{x}}^3}}}{2}\] + ...
C. 2 + 3x + x2 + \[\frac{{{{\text{x}}^3}}}{2}\] + ...
D. 2 - 3x - x2 + \[\frac{{{{\text{x}}^3}}}{2}\] + ...
B. \[\infty \]
C. \[\frac{1}{2}\]
D. \[ - \infty \]
A. \[1 + \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
B. \[ - 1 - \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
C. \[1 - \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
D. \[ - 1 + \frac{{{{\left( {{\text{x}} - \pi } \right)}^2}}}{{3!}} + ...\]
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