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Evaluate the following one sided limit:
\[\lim_{x \to \frac{\pi}{2}} \tan x\]
Concept: undefined >> undefined
Evaluate the following one sided limit:
\[\lim_{x \to 0^-} \frac{x^2 - 3x + 2}{x^3 - 2 x^2}\]
Concept: undefined >> undefined
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Evaluate the following one sided limit:
\[\lim_{x \to - 2^+} \frac{x^2 - 1}{2x + 4}\]
Concept: undefined >> undefined
Evaluate the following one sided limit:
\[\lim_{x \to 0^-} 2 - \cot x\]
Concept: undefined >> undefined
Evaluate the following one sided limit:
\[\lim_{x \to 0^-} 1 + cosec x\]
Concept: undefined >> undefined
Show that \[\lim_{x \to 0} e^{- 1/x}\] does not exist.
Concept: undefined >> undefined
Find: \[\ \lim_{x \to 2} \left[ x \right]\]
Concept: undefined >> undefined
Find: \[ \lim_{x \to \frac{5}{2}} \left[ x \right]\]
Concept: undefined >> undefined
Find: \[ \lim_{x \to 1} \left[ x \right]\]
Concept: undefined >> undefined
Prove that \[\lim_{x \to a^+} \left[ x \right] = \left[ a \right]\] R. Also, prove that \[\lim_{x \to 1^-} \left[ x \right] = 0 .\]
Concept: undefined >> undefined
Show that \[\lim_{x \to 2^-} \frac{x}{\left[ x \right]} \neq \lim_{x \to 2^+} \frac{x}{\left[ x \right]} .\]
Concept: undefined >> undefined
Find \[\lim_{x \to 3^+} \frac{x}{\left[ x \right]} .\] Is it equal to \[\lim_{x \to 3^-} \frac{x}{\left[ x \right]} .\]
Concept: undefined >> undefined
Find \[\lim_{x \to 5/2} \left[ x \right] .\]
Concept: undefined >> undefined
Evaluate \[\lim_{x \to 2} f\left( x \right)\] (if it exists), where \[f\left( x \right) = \left\{ \begin{array}{l}x - \left[ x \right], & x < 2 \\ 4, & x = 2 \\ 3x - 5, & x > 2\end{array} . \right.\]
Concept: undefined >> undefined
Show that \[\lim_{x \to 0} \sin \frac{1}{x}\]does not exist.
Concept: undefined >> undefined
Let \[f\left( x \right) = \begin{cases}\frac{k\cos x}{\pi - 2x}, & where x \neq \frac{\pi}{2} \\ 3, & where x = \frac{\pi}{2}\end{cases}\] and if \[\lim_{x \to \frac{\pi}{2}} f\left( x \right) = f\left( \frac{\pi}{2} \right)\]
Concept: undefined >> undefined
Classify the following pair of line as coincident, parallel or intersecting:
2x + y − 1 = 0 and 3x + 2y + 5 = 0
Concept: undefined >> undefined
Classify the following pair of line as coincident, parallel or intersecting:
x − y = 0 and 3x − 3y + 5 = 0]
Concept: undefined >> undefined
Classify the following pair of line as coincident, parallel or intersecting:
3x + 2y − 4 = 0 and 6x + 4y − 8 = 0.
Concept: undefined >> undefined
Prove that the lines \[\sqrt{3}x + y = 0, \sqrt{3}y + x = 0, \sqrt{3}x + y = 1 \text { and } \sqrt{3}y + x = 1\] form a rhombus.
Concept: undefined >> undefined
