Limits And Derivatives CBSE Questions & Answers

\(\mathop {Lt}\limits_{x \to \infty } {{\mathop {\Sigma \;r}\limits_{r = 1}^n } \over {{n^2}}}\) is equal to

\(\mathop {Lt}\limits_{n \to \infty } {{\mathop \Sigma \limits_{r = 1}^n {r^2}} \over {{n^3}}}\) is equal to

\(\mathop {Lt}\limits_{x \to 0} \;{1 \over x}\)

\(\mathop {Lt}\limits_{x \to 0} \;\;x\left[ x \right]\) is equal to

\(\mathop {Lt}\limits_{x \to 0} \;\;{{{{(1 + x)}^n} - 1} \over x}\) is equal to

\(\mathop {Lt}\limits_{n \to \infty } \;\;\left[ {{1 \over {1 - {n^2}}} + {2 \over {1 - {n^2}}} + {3 \over {1 - {n^2}}} + ...{n \over {1 - {n^2}}}} \right]\) is equal to

\(\mathop {Lt}\limits_{h \to 0} \;{{{{\sin }^2}(x + h) - {{\sin }^2}x} \over h}\) is equal to

If a is a real number, then \(\mathop {Lt}\limits_{x \to a} \;\;\;{{\left| {x - a} \right|} \over {x - a}}\)

If k be a integer, then \(\mathop {Lt}\limits_{x \to {k^ + }} \;\;(x - \left[ x \right])\) is equal to

\(\mathop {Lt}\limits_{x \to {a^ - }^ - } \;\;{{\left| {x - a} \right|} \over {x - a}}\) is equal to

If k be an integer, then \(\mathop {Lt}\limits_{x \to {k^ - }^{}} \;\;(x - \left[ x \right])\) is equal to

\(\mathop {Lt}\limits_{x \to 0} \;\;\left( {{{\tan x - x} \over x}} \right)\sin \left( {{1 \over x}} \right)\) is equal to

\(\mathop {Lt}\limits_{x \to 3} \;\;{{\sqrt {{x^2} + 10} - \sqrt {19} } \over {x - 3}}\) is equal to

Maximum value of \({x^3} - 3x + 2in\left[ {0,2} \right]\) is

\(\mathop {Lt}\limits_{x \to 0 + } {{\sqrt x } \over {\sqrt {16 + \sqrt x } - 4}}\)