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Is f(x)=x+sinxf(x)= x + \sin xf(x)=x+sinx an injective function?
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∑j=0∞∑i=0∞2−(i+j)i+j+1= ?\large\sum _{ j=0 }^{ \infty }{ \sum _{ i=0 }^{ \infty }{ \frac { { 2 }^{ -(i+j) } }{ i+j+1 } } } = \ ?j=0∑∞i=0∑∞i+j+12−(i+j)= ?
Give your answer to 3 decimal places.
limxy→1(ln xln y+ln yln x)= ? \large \lim _{xy\to 1}\left(\frac{\ln\:x}{\ln\:y}+\frac{\ln\:y}{\ln\:x}\right)= \ ? xy→1lim(lnylnx+lnxlny)= ?
2×limh→0∫11+hxx dx−∫1−h1xx dxh2= ? \large 2 \times \lim_{h\to0} \dfrac{\int_1^{1+h} x^x \, dx - \int_{1-h}^1 x^x \, dx }{h^2} =\, ? 2×h→0limh2∫11+hxxdx−∫1−h1xxdx=?
Some people claim that 00=1 0 ^ 0 = 1 00=1. What is
limx→0+x1lnx? \Large \lim_{ x \rightarrow 0^+ } x ^{^ { \frac{ 1}{\ln x} }}?x→0+limxlnx1?
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