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Please help me! I kept using L'Hôpital's rule millions of times and I can't evaluate the limit below!
limx→0cotxcscx= ? \displaystyle \lim_{x \to 0} \frac {\cot x }{\csc x } = \, ? x→0limcscxcotx=?
Details and Assumptions:
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limx→1xn+xn−1+…+x−nx−1= ?\large \lim_{x \to 1}\frac {x^{n} + x^{n-1} + \ldots + x - n}{x - 1} = \ ? x→1limx−1xn+xn−1+…+x−n= ?
If the limit
limx→0(sin2xx3+a+bx2)=0\lim _{ x\rightarrow 0 }{ \left( \frac { \sin { 2x } }{ { x }^{ 3 } } +a+\frac { b }{ { { x }^{ 2 } } } \right) } =0x→0lim(x3sin2x+a+x2b)=0
is true for constants aaa and bbb, then what is the value of 3a+b?3a+b?3a+b?
limx→0(1x4−∫0x2e−u2dux6)= ? \lim_{x \to 0} \left(\frac{1}{x^4} - \frac{ {\displaystyle\int_{0}^{x^2}} e^{-u^2} du}{x^6}\right) = \, ? x→0lim⎝⎜⎜⎜⎛x41−x6∫0x2e−u2du⎠⎟⎟⎟⎞=?
What is the value of
limx→0tanx−xsinx−x? \lim _{ x \rightarrow 0 } \frac{ \tan x - x } { \sin x - x }? x→0limsinx−xtanx−x?
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